Question

which of the binomials below is a factor of this trinomial?
$x^2 - 5x - 14$
a. $x-1$
b. $x-7$
c. $x-2$
d. $x-14$

Explanation:

Step1: Find pair of factors for -14

We need two numbers that multiply to $-14$ and add to $-5$. The pair is $-7$ and $2$, since $(-7)\times2=-14$ and $-7+2=-5$.

Step2: Factor the trinomial

Rewrite the trinomial using the factor pair:
$$x^2 -5x -14=(x-7)(x+2)$$

Answer:

B. $x-7$