Question

write the function in factored form. check by multiplication.
\\( y = -2x^3 - 2x^2 + 112x \\)
\\( y = \square \\) (factor completely.)

Explanation:

Step1: Factor out GCF

Factor $-2x$ from all terms.
$y = -2x(x^2 + x - 56)$

Step2: Factor quadratic trinomial

Find two numbers that multiply to $-56$ and add to $1$, then factor.
$x^2 + x - 56 = (x + 8)(x - 7)$

Step3: Verify by multiplication

Multiply the factored terms to check.
$-2x(x + 8)(x - 7) = -2x(x^2 - 7x + 8x - 56) = -2x(x^2 + x - 56) = -2x^3 -2x^2 +112x$

Answer:

$y = -2x(x + 8)(x - 7)$