Use the Factor Theorem to determine if the given binomial is a factor of the given polynomial function: f(x)=2x^3+x^2-5x+2; x+2 (MULTIPLE CHOICE)

Question

Use the Factor Theorem to determine if the given binomial is a factor of the given polynomial function:

f(x)=2x³+x²-5x+2; x+2

 

a. f(-2)=0; yes, the binomial is a factor of the polynomial.
b. f(-2)≠0; the binomial is not a factor of the polynomial.
c. f(2)=0; yes, the binomial is a factor of the polynomial.
d. f(2)≠0; the binomial is not a factor of the polynomial.

Answer 1

The Factor Theorem says that if f(x) is a polynomial function, then   x - c is a factor of f(x) if and only if f(c) = 0.  

 

For the given function, f(-2) = 2(-2)³ + (-2)² - 5(-2) + 2

 

                                                  = -16 + 4 + 10 + 2 = 0

 

Therefore, by the Factor Theorem, x - (-2) [that is, x + 2] is a factor of f(x).  

 

ANSWER:  (a)