Question

a. factor by grouping. b. divide the expression by the leading coefficient. c. examine the signs of coefficients to determine the signs of the factors. d. split the middle term, writing it as the sum of two factors of 30. now split the middle term of the given expression so that they are sum of the factors of 30. 17x = 2x + 15x now factor by grouping. 10x² + 17x + 3 = 10x² + 2x + 15x + 3 = □(5x + 1) + 3(□)

Explanation:

Step1: Factor first two terms

Factor $2x$ from $10x^2 + 2x$:
$10x^2 + 2x = 2x(5x + 1)$

Step2: Factor last two terms

Factor $3$ from $15x + 3$:
$15x + 3 = 3(5x + 1)$

Step3: Substitute back to expression

Replace factored parts into the rewritten polynomial:
$10x^2 + 2x + 15x + 3 = 2x(5x + 1) + 3(5x + 1)$

Answer:

First blank: $2x$
Second blank: $5x + 1$