Question

trinomial
$x^2 + bx + c$
find factors of c
that add up to b
example(s):

• $x^2 - x - 42$
• $2w^2 + 20w + 50$

Explanation:

Step1: Factor first trinomial $x^2 - x - 42$

Identify $b=-1$, $c=-42$. Find factors of $-42$ that sum to $-1$: $-7$ and $6$.
Rewrite and factor:
$x^2 -7x +6x -42 = x(x-7)+6(x-7)=(x-7)(x+6)$

Step2: Factor second trinomial $2w^2 +20w +50$

First factor out GCF 2:
$2(w^2 +10w +25)$
Identify $b=10$, $c=25$. Find factors of 25 that sum to 10: $5$ and $5$.
Factor the inner trinomial:
$w^2 +5w +5w +25 = w(w+5)+5(w+5)=(w+5)^2$
Combine with GCF: $2(w+5)^2$

Answer:

1. $\boldsymbol{(x-7)(x+6)}$
2. $\boldsymbol{2(w+5)^2}$