Question

Please factor the following cubic polynomial using the grouping technique. Show all work necessary. et/?f=x%5E3-8x%5E2%2B7x-56" id="TexFormula1" title="x^3-8x^2+7x-56" alt="x^3-8x^2+7x-56" align="absmiddle" class="latex-formula">

Answer 1

$\text{Hello! :)}$

$\large\boxed{(x - 8)(x^{2} + 7)}$

$x^{3} - 8x^{2} + 7x - 56\\ \\\text{Factor by grouping:}\\\\\text{Take "x" out of the first and third, and -8 from the second and last terms}\\\\x(x^{2} +7) -8(x^{2} + 7)\\\\\text{Rewrite:}\\\\(x - 8)(x^{2} + 7)$

Answer 2

Answer: (x²+7)(x-8)

Step-by-step explanation:

When grouping polynomials, you want to split the polynomial in half. Then you would factor each part. At the end, you should have the same expression in the parentheses, and pair them together.

x³-8x²+7x-56                       [split polynomial]

(x³-8x²)+(7x-56)                   [factor each part]

x²(x-8)+7(x-8)                       [if you notice, the expression in the parentheses are the same]

(x²+7)(x-8)

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Check: Correct

(x²+7)(x-8)                            [distribute by FOIL]

x³-8x²+7x-56

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After factoring and checking our work, we know that (x²+7)(x-8) is x³-8x²+7x-56 factored.