3. Q3a
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Similar Question 1
<p>Factor if possible.</p><p><code class='latex inline'>\displaystyle 20 a^{2}-180 </code></p>
Similar Question 2
<p>Determine two values of <code class='latex inline'>k</code> so that expression can be factored as a difference of squares.</p><p><code class='latex inline'>\displaystyle 16d^2 -k </code></p>
Similar Question 3
<p>Determine two values of <code class='latex inline'>k</code> so that the trinomial can be factored as a difference of squares.</p><p><code class='latex inline'>\displaystyle a^2 -kb^2 </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>Factor.</p><p>a) <code class='latex inline'>\displaystyle 5k - 35 </code></p><p>b) <code class='latex inline'>4h^2 -20h</code></p><p>c) <code class='latex inline'>2xy - 8xy^2</code></p><p>d) <code class='latex inline'>x^2 - 25</code></p><p>e) <code class='latex inline'>1 - 49 m^2</code></p><p>f) <code class='latex inline'>4a^2 - 16b^2</code></p>
<p>Factor each polynomial.</p><p><code class='latex inline'>\displaystyle 51 c^{3}-34 c </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle (2 x-y)^{2}-9 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle x^{2}-36 </code></p>
<p>Determine the missing factor.</p><p><code class='latex inline'>\displaystyle x^{2}-25=(x+5)(?) </code></p>
<p>State the missing factor.</p><p><code class='latex inline'>\displaystyle x^{2}-25=(x+5)(?) </code></p>
<p>Determine all integers, <code class='latex inline'>\displaystyle m </code> and <code class='latex inline'>\displaystyle n </code>, such that <code class='latex inline'>\displaystyle m^{2}-n^{2}=24 </code></p>
<p>Factor if possible.</p><p><code class='latex inline'>\displaystyle 16-36 x^{2} </code></p>
<p>Factor each expression.</p><p><code class='latex inline'>\displaystyle x^4 -16 </code></p>
<p>Determine two values of <code class='latex inline'>k</code> so that each trinomial can be factored as a difference of squares.</p><p><code class='latex inline'>49c^2-k</code></p>
<p>Factor fully.</p><p><code class='latex inline'>\displaystyle (x + y)^2 -64 </code></p>
<p>Determine all integers, <code class='latex inline'>\displaystyle m </code> and <code class='latex inline'>\displaystyle n </code>, such that <code class='latex inline'>\displaystyle m^{2}-n^{2}=45 </code></p>
<p>Find the factored forms of each expression. Check your answer.</p><p><code class='latex inline'>\displaystyle 3 s^{2}+75 </code></p>
<p>Find the factored forms of each expression. Check your answer.</p><p><code class='latex inline'>\displaystyle x^{2}+25 </code></p>
<p>Determine two values of <code class='latex inline'>k</code> so that each trinomial can be factored as a difference of squares.</p><p><code class='latex inline'>ky^2-16</code></p>
<p>Determine two values of <code class='latex inline'>k</code> so that each trinomial can be factored as a difference of squares.</p><p><code class='latex inline'>m^2-kn^2</code></p>
<p>Find the factored forms of each expression. Check your answer.</p><p><code class='latex inline'>\displaystyle x^{2}+\frac{1}{4} </code></p>
<p>Factor fully.</p><p><code class='latex inline'>\displaystyle 5 x^{2}-5 </code></p>
<p>Determine two values of <code class='latex inline'>k</code> so that each trinomial can be factored as a difference of squares.</p><p><code class='latex inline'>64m^2-k</code></p>
<p>Determine the missing factor.</p><p><code class='latex inline'>\displaystyle 9 x^{2}-64=(?)(3 x+8) </code></p>
<img src="/qimages/63614" /><p>If a right triangle has one side of length 8 units, possible whole-number lengths of the other side and the hypotenuse can be found as follows. List pairs of whole numbers whose product is <code class='latex inline'>\displaystyle 8^{2} </code> or <code class='latex inline'>\displaystyle 64 . </code></p><p><code class='latex inline'>\displaystyle \begin{array}{ll}64=64 \times 1 & 64=16 \times 4 \\ 64=32 \times 2 & 64=8 \times 8\end{array} Then, find whether each pair of whole numbers represents the product of the sum and difference of two whole numbers. \begin{array}{rlrl}64 & =32 \times 2 & 64 & =16 \times 4 \\ & =(17+15)(17-15) & & =(10+6)(10-6) \\ & =17^{2}-15^{2} & & =10^{2}-6^{2}\end{array} </code></p><p>For the products <code class='latex inline'>\displaystyle 64 \times 1 </code> and <code class='latex inline'>\displaystyle 8 \times 8 </code>, there are no pairs of whole numbers with either a sum of 64 and a difference of 1, or a sum of 8 and a difference of 8 . Thus, if a right triangle has one side of length 8 units, the other side and the hypotenuse could measure 6 units and 10 units, or 15 units and 17 units.</p><p>a) Find the possible whole-number lengths of the second side and the hypotenuse for each of the following right triangles.</p><p>b) Communication Explain why the method works.</p>
<p>Factor each expression. Remember to divide out all common factors first.</p><p><code class='latex inline'>\displaystyle 2 x^{2}-18 </code></p>
<p>Factor each polynomial.</p><p><code class='latex inline'>\displaystyle 40 a^{2}-32 a </code></p>
<p>Determine two values of <code class='latex inline'>k</code> so that expression can be factored as a difference of squares.</p><p><code class='latex inline'>\displaystyle 16d^2 -k </code></p>
<p>Factor each polynomial.</p><p><code class='latex inline'>\displaystyle 9 x^{2}-25 </code></p>
<p>The binomial <code class='latex inline'> 16-81 n^{4} </code> can be factored twice using the difference-of-squares rule.</p><p>a. Factor <code class='latex inline'> 16-81 n^{4} </code> completely.</p><p>b. Reasoning What characteristics do 16 and <code class='latex inline'> 81 n^{4} </code> share that make this possible?</p><p>c. Open-Ended Write another binomial that can be factored twice using the difference of squares rule.</p>
<p>Determine two values of <code class='latex inline'>k</code> so that the polynomial can be factored as a difference of squares.</p><p><code class='latex inline'>\displaystyle km^2 -25 </code></p>
<p>Find the factored forms of each expression. Check your answer.</p><p><code class='latex inline'>\displaystyle 4 b^{2}+1 </code></p>
<p>Find the factored forms of each expression. Check your answer.</p><p><code class='latex inline'>\displaystyle -9 x^{2}-100 </code></p>
<p>Determine two values of <code class='latex inline'>k</code> so that the trinomial can be factored as a difference of squares.</p><p><code class='latex inline'>\displaystyle a^2 -kb^2 </code></p>
<p>Factor fully, if possible.</p><p><code class='latex inline'>\displaystyle 3 b^{2}-300 </code></p>
<p>Factor if possible.</p><p><code class='latex inline'>\displaystyle x^{2}-121 </code></p>
<p>Determine two values of <code class='latex inline'>k</code> so that each trinomial can be factored as a difference of squares.</p><p><code class='latex inline'>a^2-kb^2</code></p>
<p>Factor each expression. Remember to divide out all common factors first.</p><p><code class='latex inline'>\displaystyle 15 c^{3}+25 c^{2} </code></p>
<p>Factor fully.</p><p><code class='latex inline'>\displaystyle 3 y^{2}-27 </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle 100 x^{2}-9 y^{2} </code></p>
<p>Find the factored forms of each expression. Check your answer.</p><p><code class='latex inline'>\displaystyle x^{2}+1 </code></p>
<p>Factor.</p><p> <code class='latex inline'>\displaystyle 121 x^{2}-25 </code></p>
<p>Determine two values of <code class='latex inline'>k</code> so that each trinomial can be factored as a difference of squares.</p><p><code class='latex inline'>kx^2-9</code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle x^{2}-64 </code></p>
<p>Factor if possible.</p><p><code class='latex inline'>\displaystyle 20 a^{2}-180 </code></p>
<p>Calculate mentally.</p><p><code class='latex inline'>\displaystyle 34^{2}-24^{2} </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle x^{4}-81 </code></p>
<p>Factor each expression.</p> <ul> <li>i) <code class='latex inline'>\displaystyle x^4 -1 </code></li> <li>ii) <code class='latex inline'>\displaystyle x^4 -16 </code></li> <li>iii) <code class='latex inline'>\displaystyle x^5 -1 </code></li> <li>iv) <code class='latex inline'>\displaystyle x^5 -32 </code></li> </ul>
<p>Fred claims that the difference between the squares of any two consecutive odd numbers is 4 times their median. For example, <code class='latex inline'>\displaystyle \begin{aligned} 9^{2}-7^{2} &=81-49 \\ &=32=4(8) \\ </code><code class='latex inline'>\displaystyle \begin{aligned} 15^{2}-13^{2} &=225-169 \\ &=56 &=4(14) \end{aligned} </code><code class='latex inline'>\displaystyle \end{aligned} </code> Use variables to explain why Fred is correct.</p>
<p>Determine two values of <code class='latex inline'>k</code> so that each trinomial can be factored as a difference of squares.</p><p><code class='latex inline'>36p^2-kq^2</code></p>
<p>Calculate mentally.</p><p><code class='latex inline'>\displaystyle 52^{2}-48^{2} </code></p>
<p>Factor.</p><p><code class='latex inline'>\displaystyle x^{2}-100 </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 49y^2 - 9 </code></p>
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