Question

this is a multi - part item.
factor the polynomial.
x² + 5x - 14 = a (x - 2) ✔ × b (x + 7) ✔
x² - 10x + 16 = c (x - 2) ✔ × d (x - 8) ✔
which polynomial is a factor of both expressions?
options: x + 7, x - 8, (x - 2)², x - 2

Explanation:

Step1: Identify factors of each polynomial

First polynomial: \(x^2 + 5x - 14\) factors into \((x - 2)(x + 7)\) (as marked A and B).
Second polynomial: \(x^2 - 10x + 16\) factors into \((x - 2)(x - 8)\) (as marked C and D).

Step2: Find common factor

Compare the factors of both polynomials. The common factor is \((x - 2)\) (or \(x - 2\) when simplified, since \((x - 2)^2\) is not a factor of the first polynomial).

Answer:

\(x - 2\) (or the option labeled with \(x - 2\))