Question

factor the following trinomial.
$5x^2 + 2x - 7$
$(5x + ?)(x - \square)$

Explanation:

Step1: Identify trinomial structure

Given trinomial: $5x^2 + 2x - 7$, factored form template: $(5x + a)(x - b)$

Step2: Expand factored template

$(5x + a)(x - b) = 5x^2 -5bx + ax - ab = 5x^2 + (a-5b)x - ab$

Step3: Match coefficients to solve

Set up equations:

1. $a - 5b = 2$
2. $ab = 7$

Test integer values for $a,b$ (since 7 is prime): $a=7, b=1$
Check: $7 - 5(1) = 2$, which matches; $7*1=7$, which matches.

Answer:

The missing values are 7 and 1, so the fully factored trinomial is $(5x + 7)(x - 1)$