Question

the polynomial $10x^3 + 35x^2 - 4x - 14$ is factored by grouping.
$10x^3 + 35x^2 - 4x - 14$
$5x^2(\\_\\_\\_\\_) - 2(\\_\\_\\_\\_)$
what is the common factor that is missing from both sets of parentheses?
○ $-2x - 7$
○ $2x + 7$
○ $-2x^2 + 7$
○ $2x^2 + 7$

Explanation:

Step1: Factor first two terms

Take $5x^2$ from $10x^3+35x^2$:
$10x^3 + 35x^2 = 5x^2(2x + 7)$

Step2: Factor last two terms

Take $-2$ from $-4x-14$:
$-4x - 14 = -2(2x + 7)$

Step3: Identify common factor

Compare the two factored parts to find the shared expression.

Answer:

B. $2x + 7$