Question

Identify the binomial that is not a factor of the polynomial P(x) = 2x3 − 7x2 − 10x + 24.

2x − 3
x − 4
x + 2
x + 3

Answer 1

(x + 3)

Explanation:

NOTE: first we need to understand this :

(x + a) is factor of the polynomial only if P(-a) = 0

and

(x - a) is factor of the polynomial only if P(a) = 0

• P(-3) = 2×(-3)³ - 7×(-3)² - 10×(-3) + 24

= -63

then (x + 3) is not a factor

• now, we can prove that the others are factors, for instance (x + 2)

P(-2) = 2×(-2)³ - 7×(-2)² - 10×(-2) + 24

= 0

then (x + 2) is a factor.

:)