Question

which expression is equal to the polynomial below?
$2x^4 + 5x^3 - 8x - 20$
$x^3(2x + 5) + 4(2x - 5)$
$x^3(2x + 5) - 4(2x + 5)$
$x^3(2x - 5) - 4(2x - 5)$
$x^3(2x + 5) + 4(2x + 5)$
done

Explanation:

Step1: Expand Option 1

$x^3(2x + 5) + 4(2x - 5) = 2x^4 + 5x^3 + 8x - 20$

Step2: Expand Option 2

$x^3(2x + 5) - 4(2x + 5) = 2x^4 + 5x^3 - 8x - 20$

Step3: Expand Option 3

$x^3(2x - 5) - 4(2x - 5) = 2x^4 - 5x^3 - 8x + 20$

Step4: Expand Option 4

$x^3(2x + 5) + 4(2x + 5) = 2x^4 + 5x^3 + 8x + 20$

Step5: Match to target polynomial

Compare expanded results to $2x^4 + 5x^3 - 8x - 20$

Answer:

$x^3(2x + 5) - 4(2x + 5)$