Question

the polynomial $10x^3 + 35x^2 - 4x - 14$ is factored by grouping.
$10x^3 + 35x^2 - 4x - 14$
$5x^2(\underline{quadquad}) - 2(\underline{quadquad})$
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

Factor \(10x^3 + 35x^2\). The GCF of \(10x^3\) and \(35x^2\) is \(5x^2\). So, \(10x^3 + 35x^2 = 5x^2(2x + 7)\).

Step2: Factor last two terms

Factor \(-4x - 14\). The GCF of \(-4x\) and \(-14\) is \(-2\). So, \(-4x - 14 = -2(2x + 7)\).

Step3: Match the blanks

From the factored forms, the first blank (after \(5x^2\)) and the second blank (after \(-2\)) should both be \(2x + 7\).

Answer:

\(2x + 7\) (the option corresponding to "2x + 7")