Question

determine the product of linear and quadratic factors. verify graphically that the expressions are equivalent.
sample problem
$x(x^2 + 3x - 4)$
$x(x^2 + 3x - 4) = x^3 + 3x^2 - 4x$
the graph of the original expression and the graph of the final expression are the same. so the expressions are equivalent.

type the answer in the space provided. use numbers instead of words.

$(2x - 9)(4x^2 - 5x - 12)$
$=\square$

Explanation:

Step1: Distribute $2x$ to quadratic term

$2x(4x^2 - 5x - 12) = 8x^3 - 10x^2 - 24x$

Step2: Distribute $-9$ to quadratic term

$-9(4x^2 - 5x - 12) = -36x^2 + 45x + 108$

Step3: Combine the two results

$(8x^3 - 10x^2 - 24x) + (-36x^2 + 45x + 108)$

Step4: Combine like terms

$8x^3 + (-10x^2 - 36x^2) + (-24x + 45x) + 108 = 8x^3 - 46x^2 + 21x + 108$

Answer:

$8x^3 - 46x^2 + 21x + 108$