Determine if x + 3 is a factor of -3x^3+6x^2+6x+9. How do you know? (MULTIPLE CHOICE)

Question

Determine if x + 3 is a factor of -3x³+6x²+6x+9. How do you know?

 

a. yes, because the remainder is 126
b. no, because the remainder is –108
c. yes, because the remainder is –108
d. no, because the remainder is 126

 

Choose one thanks

Answer 1

By the Remainder Theorem,  the remainder when a polynomial function, f(x), is divided by x - c is f(c).  

 

x + 3 = x - (-3)

f(x) = the given polynomial

 

The remainder when f(x) is divided by x - (-3) = f(-3)

                                                                                  = 126

 

Since the remainder is nonzero, x + 3 is NOT a factor of f(x).

 

ANSWER:  d