11. Q11
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Similar Question 1
<p>Is this statement true or false? If the statement is false, reword it to make it true.</p> <ul> <li>All polynomial equations can be solved algebraically.</li> </ul>
Similar Question 2
<p>Is this statement true or false? If the statement is false, reword it to make it true.</p> <ul> <li>All the roots of a polynomial equation correspond to the x-int of the graph of the corresponding polynomial function.</li> </ul>
Similar Question 3
<p>Determine the real roots of each polynomial equation.</p><p><code class='latex inline'>(x^2- 1)(x^2 + 4) = 0</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>Open-top boxes are constructed by cutting equal squares from the corners of cardboard sheet that measure 32 cm by 28 cm. Determine possible dimensions of the boxes if each has a volume of <code class='latex inline'>1920 cm^3.</code></p>
<p>Solve by factoring.</p><p><code class='latex inline'>x^3 + x^2 - 8x - 12 = 0</code></p>
<p>Is this statement true or false? If the statement is false, reword it to make it true.</p> <ul> <li>If the graph of a quartic function has two x-intercepts, then the corresponding quartic equation has four real roots.</li> </ul>
<p>Determine the real roots of each polynomial equation.</p><p><code class='latex inline'>(x^2- 1)(x^2 + 4) = 0</code></p>
<p>Solve by factoring.</p><p><code class='latex inline'>8x^4 - 64x= 0</code></p>
<p>Solve for x.</p><p><code class='latex inline'> \displaystyle (x - 1)(x - 4)(x + 3) = 0 </code></p>
<p>Solve for x.</p><p><code class='latex inline'> \displaystyle (5x - 8)(x + 3)(2x - 1) = 0 </code></p>
<p>Determine the x-intercepts of the graph of each polynomial function.</p><p><code class='latex inline'>y = x^3 - 4x^2 - 45x</code></p>
<p>Determine the real roots of each polynomial equation.</p><p><code class='latex inline'>(x^2 +1)(x - 4) = 0</code></p>
<p>Solve by factoring.</p><p><code class='latex inline'>4x^4 - 2x^3 - 16x^2 + 8x = 0</code></p>
<p>Solve for <code class='latex inline'>x</code>.</p><p><code class='latex inline'> \displaystyle x(x +2)(x - 5) = 0 </code></p>
<p>Determine the x-intercepts of the graph of each polynomial function.</p><p><code class='latex inline'>y = x^4 - 16</code></p>
<p>Solve by factoring.</p><p><code class='latex inline'>x^4 + 13x^3 = -36</code></p>
<p>Factor <code class='latex inline'>x^6 - 1</code> using the following formula: <code class='latex inline'>(x -a)(x^{n-1}+x^{n-2}a + x^{n-3}a^2 + ... + xa^{n-2} + a^{n-1})</code></p>
<p>Is this statement true or false? If the statement is false, reword it to make it true.</p> <ul> <li>All the roots of a polynomial equation correspond to the x-int of the graph of the corresponding polynomial function.</li> </ul>
<p>Determine the real roots of each polynomial equation.</p><p><code class='latex inline'>(4x^2 - 9)(x^2 + 16) = 0</code></p>
<p>Solve for x.</p><p><code class='latex inline'> \displaystyle (2x - 5)(2x + 5)(x - 7) = 0 </code></p>
<p>Is it possible for a polynomial equation to have exactly one non-real root? </p>
<p>Determine the real roots of each polynomial equation.</p><p><code class='latex inline'>(x^4 - 1)(x^2 - 25) = 0</code></p>
<p>Solve by factoring.</p><p><code class='latex inline'>x^4 - x^3 = 2x + 4</code></p>
<p>Solve by factoring.</p><p><code class='latex inline'>2x^3 + 3x^2 - 5x - 6 = 0</code></p>
<p>Solve for x.</p><p><code class='latex inline'> \displaystyle (x - 7)(3x + 2)(x + 1) = 0 </code></p>
<p>Solve by factoring.</p><p><code class='latex inline'>x^4 - x^3 - 11x^2 + 9x + 18 = 0</code></p>
<p>Solve by factoring.</p><p><code class='latex inline'>2x^3 - 7x^2 + 10x - 5 = 0</code></p>
<p>Use the graph to determine the roots of the corresponding polynomial equation. The roots are all integral values.</p><img src="/qimages/311" />
<p>Factor and find all the roots of</p><p><code class='latex inline'> \displaystyle f(x) = (2x^2 - x -1)(x^2 -3x -4) </code></p>
<p>Use the graph to determine the roots of the corresponding polynomial equation. The roots are all integral values.</p><img src="/qimages/313" />
<p>A steel beam is supported by two vertical walls. When a 1000-kg weight is placed on the beam, x metres from one end, the vertical deflection, d, in metres, can be calculated using the formula <code class='latex inline'>d(x) = 0.0005(x^4-16x^3 + 512x)</code>. How far from the end of the beam should the weight be placed for a deflection of 0 m?</p>
<p>The distance, d, in kilometres, travelled by a plane after t hours can be represented by <code class='latex inline'>d(t) = -4t^3 + 40t^2 + 500t</code>, where <code class='latex inline'>0 \leq t \leq 10</code>. How long does the plane take to fly <code class='latex inline'>4088 km</code>?</p>
<p>Is this statement true or false? If the statement is false, reword it to make it true.</p> <ul> <li>All polynomial equations can be solved graphically.</li> </ul>
<p>Determine the real roots of each polynomial equation.</p><p><code class='latex inline'>(x^2 + 7x + 12)(x^2 - 49) = 0</code></p>
<p>Use the graph to determine the roots of the corresponding polynomial equation. The roots are all integral values.</p><img src="/qimages/314" />
<p>Solve by factoring.</p><p><code class='latex inline'>x^3 - 4x^2 - 7x + 10 = 0</code></p>
<p>Is this statement true or false? If the statement is false, reword it to make it true.</p> <ul> <li>All polynomial equations can be solved algebraically.</li> </ul>
<p>Solve for x.</p><p><code class='latex inline'> \displaystyle (4x - 1)(2x - 3)(x + 8) = 0 </code></p>
<p>Solve by factoring.</p><p><code class='latex inline'>x^3 - 5x^2 + 8 = -2x</code></p>
<p>Solve by factoring.</p><p><code class='latex inline'>9x^3 + 18x^2 - 4x - 8 = 0</code></p>
<p>Use the graph to determine the roots of the corresponding polynomial equation. The roots are all integral values.</p><img src="/qimages/312" />
<p>Determine the real roots of each polynomial equation.</p><p><code class='latex inline'>(2x^2 + 5x - 3)(4x^2 - 100) = 0</code></p>
<p>Determine the x-intercepts of the graph of each polynomial function.</p><p><code class='latex inline'>y = x^4 - 81x^2</code></p>
<p>Solve by factoring.</p><p><code class='latex inline'>x^3 - 3x^2 + x + 5 = 0</code></p>
<p>Use the graph to determine the roots of the corresponding polynomial equation. The roots are all integral values.</p><img src="/qimages/310" />
<p>Determine the real roots of each polynomial equation.</p><p><code class='latex inline'>(3x^2 + 27)(x^2 - 16) = 0</code></p>
<p>Solve for x.</p><p><code class='latex inline'> \displaystyle (3x + 2)(x + 9)( x - 2) = 0 </code></p>
<p>Is this statement true or false? If the statement is false, reword it to make it true.</p> <ul> <li>A polynomial equation of degree three must have at least one real root.</li> </ul>
<p>Solve by factoring.</p><p><code class='latex inline'>x^3 - 3x^2 - 4x + 12 = 0</code></p>
<p>Solve by factoring.</p><p><code class='latex inline'>x^3 + 2x^2 - 7x + 4 = 0</code></p>
<p>Solve by factoring.</p><p><code class='latex inline'>2x^3 - 11x^2 + 12x + 9 = 0</code></p>
<p>Solve by factoring.</p><p><code class='latex inline'>x^3 - 5x^2 + 7x - 3 = 0</code></p>
<p>Solve by factoring.</p><p><code class='latex inline'>5x^3 - 8x^2 - 27x + 18 = 0</code></p>
<p>Solve by factoring.</p><p><code class='latex inline'>x^3 - x^2 = 4x + 6</code></p>
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