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?\
\\(\circ -2x - 7\\)\
\\(\circ 2x + 7\\)\
\\(\circ -2x^2 + 7\\)\
\\(\circ 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.

Answer:

B. $2x + 7$