12. Q12
Save videos to My Cheatsheet for later, for easy studying.
Video Solution
Q1
Q2
Q3
L1
L2
L3
Similar Question 1
<p>One factor is given, and one factor is missing. What is the missing factor?</p><p><code class='latex inline'>c^2-15c+56=(c-7)(\square)</code></p>
Similar Question 2
<p>Factor.</p><p><code class='latex inline'>\displaystyle m^{2}-9 m n+14 n^{2} </code></p>
Similar Question 3
<p>Factor each expression.</p><p><code class='latex inline'>x^2-4x+4</code></p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>Determine the missing factor.</p><p><code class='latex inline'>\displaystyle a^{2}+3 a-28=(?)(a+7) </code></p>
<p>Factor, if possible.</p><p><code class='latex inline'>\displaystyle 25r^2 - 20rs + 4s^2 </code></p>
<p>What is the factored form of <code class='latex inline'>\displaystyle t^{2}+6 t-27 ? </code> <code class='latex inline'>\displaystyle \begin{array}{ll}\text { A. }(t+9)(t+3) & \text { C. }(t-9)(t-3) \\ \text { B. }(t+9)(t-3) & \text { D. }(t-9)(t+3)\end{array} </code></p>
<p>Factor each expression.</p><p><code class='latex inline'>x^2-2x+1</code></p>
<p>Determine the missing factor.</p><p><code class='latex inline'>\displaystyle -8 x+x^{2}+15=(?)(x-3) </code></p>
<p>Factor each expression.</p><p><code class='latex inline'>(a-b)^2-15(a-b)+26</code></p>
<p>Determine consecutive integers <code class='latex inline'>\displaystyle b </code> and <code class='latex inline'>\displaystyle c </code>, and also <code class='latex inline'>\displaystyle m </code> and <code class='latex inline'>\displaystyle n </code>, such that <code class='latex inline'>\displaystyle x^{2}+b x+c=(x+m)(x+n) </code></p>
<p>Factor.</p><p><code class='latex inline'>2x^2 + 14x - 120</code></p>
<p>Factor each polynomial.</p><p><code class='latex inline'>\displaystyle x^{2}-9 x-22 </code></p>
<p>Factor. </p><p> <code class='latex inline'>2y^2-2y-60</code></p>
<p>Factor. </p><p><code class='latex inline'>3v^2+9v+6</code></p>
<p>Factor each expression. Remember to divide out all common factors first.</p><p><code class='latex inline'>\displaystyle x^{2}+2 x-15 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle m^{2}-9 m n+14 n^{2} </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle w^2 - w- 30 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle 6 x^{2}-19 x+10 </code></p>
<p>A factor might be common to only some terms of a polynomial, but grouping these terms sometimes allows the polynomial to be factored. For example:</p><p><code class='latex inline'>ax-ay+bx-by</code></p><p><code class='latex inline'>=a(x-y)+b(x-y)</code></p><p><code class='latex inline'>=(x-y)(a+b)</code></p><p> <code class='latex inline'>9xa+3xb+6a+2b</code></p>
<p>Factor fully.</p><p><code class='latex inline'>\displaystyle 5x^2 -16x + 3 </code></p>
<p>One factor is given, and one factor is missing. What is the missing factor?</p><p> <code class='latex inline'>x^2-2x-63=(\square)(x+7)</code></p>
<p>Factor, if possible.</p><p><code class='latex inline'>\displaystyle m^2 + 6m + 16 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle -5 x^{2}+75 x-280 </code></p>
<p>One factor is given, and one factor is missing. What is the missing factor?</p><p><code class='latex inline'>x^2+14x+45=(\square)(x+9)</code></p>
<p>Write the polynomial in factored form. </p><p><code class='latex inline'>\displaystyle 3x^2 -18x + 24 </code></p>
<p>Factor. </p><p><code class='latex inline'>a^2+8a+15</code></p>
<p>One factor is given, and one factor is missing. What is the missing factor?</p><p><code class='latex inline'>z^2-19z+90=(\square)(z-10)</code></p>
<p>What is the factored form of <code class='latex inline'>\displaystyle 9 c^{2}+30 c+25 </code> ? <code class='latex inline'>\displaystyle \begin{array}{ll}\text { A. }(3 c+5)(3 c-5) & \text { C. }(3 c+5)^{2} \\ \text { B. }(9 c+5)(c+5) & \text { D. }(3 c-5)^{2}\end{array} </code></p>
<p>Factor each polynomial.</p><p><code class='latex inline'>\displaystyle 18 x^{2}+15 x-12 </code></p>
<p>State the missing factor.</p><p><code class='latex inline'>\displaystyle n^{2}+8 n+16=(?)(n+4) </code></p>
<p>Factor each expression.</p><p><code class='latex inline'>x^4+6x^2-27</code></p>
<p>Factor each expression.</p><p><code class='latex inline'>c^2-12cd-85d^2</code></p>
<p>Factor fully</p><p><code class='latex inline'>\displaystyle 16x^2-121y^2 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle 20 x^{2}+9 x-18 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle 12 n^{2}-67 n+16 </code></p>
<p>Factor.</p><p><code class='latex inline'>x^2-10x+16</code></p>
<p>Factor each expression.</p><p><code class='latex inline'>\displaystyle x^{2}-2 x-15 </code></p>
<p>Factor fully</p><p><code class='latex inline'>\displaystyle x^2 + 16x + 64-25y^2 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle x^{2}+10 x+25 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle 2 x^{2}-9 x-5 </code></p>
<p>Factor.</p><p><code class='latex inline'>4b^2 - 36b + 72</code></p>
<p>Determine the missing factor.</p><p><code class='latex inline'>\displaystyle 3 a^{2}+10 a-8=(?)(3 a-2) </code></p>
<p>Factor each expression.</p><p><code class='latex inline'>\displaystyle x^{2}-12 x+36 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle x^{2}-24 x+144 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle y^{2}+3 y-54 </code></p>
<p>Factor.</p><p><code class='latex inline'>c^2 + 5c - 14</code></p>
<p>Factor. </p><p><code class='latex inline'>x^3+5x^2+4x</code></p>
<p>State the missing factor.</p><p><code class='latex inline'>\displaystyle 18 x^{2}+12 x+2=2(?)^{2} </code></p>
<p>Factor fully</p><p><code class='latex inline'>\displaystyle x^2 + 6x - 27 </code></p>
<p>Factor. </p><p><code class='latex inline'>x^2+5x-50</code></p>
<p>Factor, using the greatest common factor.</p><p><code class='latex inline'>4x^2-6x+2</code></p>
<p>Factor. </p><p><code class='latex inline'>3x^2 - 21x -54</code></p>
<p>Factor. </p><p> <code class='latex inline'>3x^2+24x+45</code></p>
<p>Name the common factor of the terms of the polynomial.</p><p><code class='latex inline'>3x^2-9x+12</code></p>
<p>Factor each expression.</p><p><code class='latex inline'>x^2+12xy+35y^2</code></p>
<p>One factor is given, and one factor is missing. What is the missing factor?</p><p> <code class='latex inline'>x^2+4x-32=(x-4)(\square)</code></p>
<p>State the missing factor.</p><p><code class='latex inline'>\displaystyle 4 m^{2}-12 m+9=(?)^{2} </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle 8 a^{2}-14 a-15 </code></p>
<p>Factor.</p><p> <code class='latex inline'>y^2+6y-40</code></p>
<p>Factor fully</p><p><code class='latex inline'>\displaystyle 9 - 30a + 25a^2 </code></p>
<p>Factor.</p><p><code class='latex inline'>n^2 + 7n -18</code></p>
<p>Determine the value of each symbol.</p><p><code class='latex inline'>x^2 - 7x + \blacklozenge = (x - 3)(x - \blacksquare)</code></p>
<p>Factor.</p><p><code class='latex inline'>x^3 - 6x^2 - 16x</code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle 90 x^{2}-120 x y+40 y^{2} </code></p>
<p>Factor each expression.</p><p><code class='latex inline'>18p^2-9pq+q^2</code></p>
<p>Factor.</p><p><code class='latex inline'>y^2 - 17y + 72</code></p>
<p>Explain how to determine whether or not you can factor <code class='latex inline'>9x^2 - 10x + 18</code> over the integers.</p>
<p>Identify the type of algebraic expression and the factoring strategies you would use to factor the expression.</p><p><code class='latex inline'>\displaystyle 3x^2 + 3xa -2x -2a </code></p>
<p>Factor, if possible.</p><p><code class='latex inline'>\displaystyle x^2 + 10 x + 25 </code></p>
<p>Factor.</p><p><code class='latex inline'> \displaystyle x^2 + 6x + 9 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle 6 x^{2}-15 x+6 </code></p>
<p>A factor might be common to only some terms of a polynomial, but grouping these terms sometimes allows the polynomial to be factored. For example:</p><p><code class='latex inline'>ax-ay+bx-by</code></p><p><code class='latex inline'>=a(x-y)+b(x-y)</code></p><p><code class='latex inline'>=(x-y)(a+b)</code></p><p><code class='latex inline'>(x+y)^2+x+y</code></p>
<p>Determine the missing factor.</p><p><code class='latex inline'>\displaystyle 20+27 x+9 x^{2}=(?)(3 x+5) </code></p>
<p>Factor.</p><p><code class='latex inline'> \displaystyle x^2 + 14x + 49 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle n^2 - 13n + 40 </code></p>
<p>Factor <code class='latex inline'>\displaystyle x^{4}-13 x^{2}+36 </code></p>
<p>Factor. </p><p><code class='latex inline'>z^2-16z+55</code></p>
<p>Factor.</p><p><code class='latex inline'> \displaystyle x^2 -20x + 100 </code></p>
<p>Factor each expression.</p><p><code class='latex inline'>\displaystyle x^{2}+5 x+4 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle 10 a^{2}-11 a-6 </code></p>
<p>Factor if possible.</p><p><code class='latex inline'>\displaystyle -8 x^{2}+24 x-18 </code></p>
<p>Determine the missing factor.</p><p><code class='latex inline'>\displaystyle b^{2}-b-20=(b-5)(?) </code></p>
<p>A factor might be common to only some terms of a polynomial, but grouping these terms sometimes allows the polynomial to be factored. For example:</p><p><code class='latex inline'>ax-ay+bx-by</code></p><p><code class='latex inline'>=a(x-y)+b(x-y)</code></p><p><code class='latex inline'>=(x-y)(a+b)</code></p><p> <code class='latex inline'>10x^2-5x-6xy+3y</code></p>
<p>Factor each expression.</p><p> <code class='latex inline'>x^2+6x+9</code></p>
<p>Factor each expression.</p><p><code class='latex inline'>x^2-4x-12</code></p>
<p>One factor is given, and one factor is missing. What is the missing factor?</p><p><code class='latex inline'>a^2-11a-60=(a-15)(\square)</code></p>
<p>What is the factored form of</p><p><code class='latex inline'>\displaystyle 12 x^{2} y^{3}+6 x y-2 y^{2} </code> ?</p><p>A. <code class='latex inline'>\displaystyle 2\left(6 x^{2} y^{3}+3 x y-y^{2}\right) </code></p><p>B. <code class='latex inline'>\displaystyle 2 y\left(6 x^{2} y^{2}+3 x-y\right) </code></p><p>C. <code class='latex inline'>\displaystyle -2 y\left(-6 x^{2} y^{2}-3 x+y\right) </code></p><p>D. all of the above</p>
<p>Factor each expression.</p><p> <code class='latex inline'>m^2+4mn-5n^2</code></p>
<p>Factor each expression.</p><p><code class='latex inline'>m^2-8m+16</code></p>
<p>Factor.</p><p><code class='latex inline'>3a^2 - 3a - 36</code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle x^2 -x - 12 </code></p>
<p>Factor each expression.</p><p> <code class='latex inline'>x^2+4x+3</code></p>
<p>Fully factor each expression.</p><p><code class='latex inline'>\displaystyle \left(x^{2}-x\right)+\left(x^{2}-3 x+2\right)+(x-1) </code></p>
<p>One factor is given, and one factor is missing. What is the missing factor?</p><p><code class='latex inline'>b^2+2b-48=(\square)(b+8)</code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle x^{2}+4 x+4 </code></p>
<p>Factor each expression.</p><p><code class='latex inline'>a^4+10a^2+9</code></p>
<p>Factor each polynomial.</p><p><code class='latex inline'>\displaystyle 15 x^{2}+7 x-2 </code></p>
<p>Factor.</p><p><code class='latex inline'>x^2 + 8x - 33</code></p>
<p>Factor fully</p><p><code class='latex inline'>\displaystyle 5x^2 - 5x - 100 </code></p>
<p>Factor.</p><p><code class='latex inline'>b^2 - 10b - 11</code></p>
<p>Factor if possible.</p><p><code class='latex inline'>\displaystyle (x+1)^{2}+4(x+1)+4 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle x^2 + 2x - 18 </code></p>
<p>One factor is given, and one factor is missing. What is the missing factor?</p><p><code class='latex inline'>y^2-10y-44=(a-15)(\square)</code></p>
<p>Write two different trinomials that have <code class='latex inline'>x + 2</code> as a factor.</p>
<p>Factor.</p><p><code class='latex inline'>x^2 - 14x + 45</code></p>
<p>Factor fully</p><p><code class='latex inline'>\displaystyle x^2 - 7x - 60 </code></p>
<p>Colin says that the greatest common factor of <code class='latex inline'>-8x^2+4x-6</code> is <code class='latex inline'>2</code>, but Colleen says that it is <code class='latex inline'>-2</code>. Explain why both answers could be considered correct.</p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle 4 x^{2}-20 x y+25 y^{2}-4 z^{2} </code></p>
<p>Factor.</p><p> <code class='latex inline'>10x^2-5x+25</code></p>
<p>Factor each expression.</p><p><code class='latex inline'>n^2+n-6</code></p>
<p>Write three different quadratic trinomials that have <code class='latex inline'>(x - 2)</code> as a factor.</p>
<p>Factor.</p><p><code class='latex inline'>w^2-5w-14</code></p>
<p>Identify the type of algebraic expression and the factoring strategies you would use to factor the expression.</p><p><code class='latex inline'>\displaystyle 3x^2 - 3x - 90 </code></p>
<p>Determine the missing factor.</p><p><code class='latex inline'>\displaystyle x^{2}+9 x+14=(x+2)(?) </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle m^2 + 11m + 24 </code></p>
<p>Explain how you know that <code class='latex inline'>\displaystyle 5 x^{2}+20 x+9 </code> cannot be factored in the indicated way.</p><p><code class='latex inline'>\displaystyle \begin{array}{ll}\text { a) as }(a x+b)^{2} & \text { b) as }(a x+b)(a x-b)\end{array} </code></p>
<p>Factor.</p><p><code class='latex inline'> \displaystyle x^2 -18 x + 81 </code></p>
<p>Factor fully</p><p><code class='latex inline'>\displaystyle 20x^2+61x + 45 </code></p>
<p>Determine the missing factor.</p><p><code class='latex inline'>\displaystyle 2 x^{2}+7 x+5=(x+1)(?) </code></p>
<p>Factor each polynomial.</p><p><code class='latex inline'>\displaystyle 4 x^{2}+29 x+30 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle x^{2}+x-12 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle 6 n^{2}+13 n+7 </code></p>
<p>Write the polynomial in factored form. </p><p><code class='latex inline'>\displaystyle x^4 - 4x^3 -5x^2 </code></p>
<p>Determine the missing factor.</p><p><code class='latex inline'>\displaystyle 4 b^{2}-20 b+25=(2 b-5)(?) </code></p>
<p>Factor each expression.</p><p><code class='latex inline'>x^2-2x-3</code></p>
<p>Factor fully</p><p><code class='latex inline'>\displaystyle 2s^2+3s-5 </code></p>
<p>Identify the type of algebraic expression and the factoring strategies you would use to factor the expression.</p><p><code class='latex inline'>\displaystyle x^2 -13x +42 </code></p>
<p>Factor fully.</p><p><code class='latex inline'>\displaystyle 6n^2 -11ny-10y^2 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle 81-x^{2}+14 x-49 </code></p>
<p>Factor each polynomial.</p><p><code class='latex inline'>\displaystyle x^{2}+13 x+40 </code></p>
<p>Identify the type of algebraic expression and the factoring strategies you would use to factor the expression.</p><p><code class='latex inline'>\displaystyle 20x^2 +11x -3 </code></p>
<p>Factor, if possible.</p><p><code class='latex inline'>\displaystyle y^2 -12 y + 36 </code></p>
<p>Determine the missing factor.</p><p><code class='latex inline'>\displaystyle 4 b^{2}-4 b-15=(2 b-5)(?) </code></p>
<p>Writing Suppose you can factor <code class='latex inline'> x^{2}+b x+c </code> as <code class='latex inline'> (x+p)(x+q) </code> .</p><p>a. Explain what you know about <code class='latex inline'> p </code> and <code class='latex inline'> q </code> when <code class='latex inline'> c>0 </code> .</p><p>b. Explain what you know about <code class='latex inline'> p </code> and <code class='latex inline'> q </code> when <code class='latex inline'> c<0 </code> .</p>
<p>One factor is given, and one factor is missing. What is the missing factor?</p><p><code class='latex inline'>c^2-15c+56=(c-7)(\square)</code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle 4 x^{2}+4 x y+y^{2} </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle x^2+ 3x + 4 </code></p>
<p>What is the factored form of <code class='latex inline'>\displaystyle 6 a^{2}+13 a-5 ? </code></p><p>A. <code class='latex inline'>\displaystyle (2 a+5)(3 a-1) \quad </code> C. <code class='latex inline'>\displaystyle (3 a+5)(2 a-1) </code></p><p>B. <code class='latex inline'>\displaystyle (6 a+5)(a-1) \quad </code> D. <code class='latex inline'>\displaystyle (2 a-5)(3 a+1) </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle t^2 - 8t + 15 </code></p>
<p>Is the product of two binomials always a trinomial? Explain using examples.</p>
<p>Factor each polynomial.</p><p><code class='latex inline'>\displaystyle 3 x^{2}+12 x-36 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle 14 + 5m - m^2 </code></p>
<p>Factor each expression.</p><p> <code class='latex inline'>a^2+ab-12b^2</code></p>
<p>Factor.</p><p><code class='latex inline'>a^2-a-56</code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle (3-n)^{2}-12(3-n)+36 </code></p>
<p>Factor each expression.</p><p><code class='latex inline'>x^2+2x+1</code></p>
<p>State all the integers, <code class='latex inline'>\displaystyle m </code>, such that <code class='latex inline'>\displaystyle x^{2}+m x-13 </code> can be factored.</p>
<p>When factoring a quadratic expression of the form <code class='latex inline'>x^2 + bx + c</code>, why does it make more sense to consider the value of <code class='latex inline'>c</code> before the value of <code class='latex inline'>b</code>? Explain.</p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle a^{2}+16 a+63 </code></p>
<p>Factor.</p><p><code class='latex inline'>-2a^2-4a+6</code></p>
<p>One factor is given, and one factor is missing. What is the missing factor?</p><p><code class='latex inline'>x^2+11x+24=(x+3)(\square)</code></p>
<p>Determine the missing factor.</p><p><code class='latex inline'>\displaystyle 9 a^{2}+6 a+1=(?)(3 a+1) </code></p>
<p>Factor each expression.</p><p><code class='latex inline'>x^2-4x+4</code></p>
<p>Factor each expression.</p><p><code class='latex inline'>a^2-9a+20</code></p>
<p>Factor.</p><p><code class='latex inline'>m^2-12m+32</code></p>
<p>Factor </p><p><code class='latex inline'>\displaystyle -2x^3 + 6x^2 + 4x </code></p>
<p>Factor fully</p><p><code class='latex inline'>\displaystyle 15-2x -x^2 </code></p>
<p>A factor might be common to only some terms of a polynomial, but grouping these terms sometimes allows the polynomial to be factored. For example:</p><p><code class='latex inline'>ax-ay+bx-by</code></p><p><code class='latex inline'>=a(x-y)+b(x-y)</code></p><p><code class='latex inline'>=(x-y)(a+b)</code></p><p><code class='latex inline'>1+xy+x+y</code></p>
<p>Factor.</p><p><code class='latex inline'>-d^3 + d^2 + 30d</code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle x^{2}+6 x y+5 y^{2} </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle 36 a^{2}-60 a+25 </code></p>
<p>Determine the value of each symbol.</p><p><code class='latex inline'>x^2 - 12x + \blacksquare = (x - \blacklozenge)(x - \blacklozenge)</code></p>
<p>Factor if possible.</p><p><code class='latex inline'>\displaystyle 49 a^{2}+42 a+9 </code></p>
<p>For what values of <code class='latex inline'>k</code> is it possible to divide out a common factor from <code class='latex inline'>6x^2+kx-12</code>, but not from <code class='latex inline'>6x^2+kx+4</code>? Explain.</p>
<p>Factor, if possible.</p><p><code class='latex inline'>\displaystyle 4x^2 + 12x + 9 </code></p>
<p>One factor is given, and one factor is missing. What is the missing factor?</p><p><code class='latex inline'>x^2-10x+21=(x-7)(\square)</code></p>
<p>Factor fully.</p><p><code class='latex inline'>\displaystyle x^2 +2xy + y^2 </code></p>
<p>Factor, if possible.</p><p><code class='latex inline'>\displaystyle 5x^2 -20xy + 2y^2 </code></p>
How did you do?
Found an error or missing video? We'll update it within the hour! ðŸ‘‰
Save videos to My Cheatsheet for later, for easy studying.