Question

what is the factored form of this quadratic trinomial?
$x^2 - x - 42$
a. $(x - 6)(x + 7)$
b. $(x + 14)(x - 3)$
c. $(x - 14)(x + 3)$
d. $(x + 6)(x - 7)$

Explanation:

Step1: Find pair of factors of -42

We need two numbers that multiply to $-42$ and add to $-1$. The pair is $6$ and $-7$, since $6 \times (-7) = -42$ and $6 + (-7) = -1$.

Step2: Rewrite trinomial as factored form

Substitute the pair into the factored structure $(x+a)(x+b)$ where $a=6$ and $b=-7$.

Answer:

D. $(x + 6)(x - 7)$