Question

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
= 2x(5x + 1) + 3(5x + 1)
= □
(factor completely.)

Explanation:

Step1: Identify common binomial factor

The expression has a common factor $(5x+1)$ in both terms.
$2x(5x+1)+3(5x+1)$

Step2: Factor out the common binomial

Extract $(5x+1)$ from both terms.
$=(5x+1)(2x+3)$

Answer:

$(5x+1)(2x+3)$