SOLUTION: Is the binomial a factor of the polynomial function? {{{ f(x) = x^3 + 2x^2 - 16x - 32 }}} Select EACH correct answer. A. (x - 2) B. (x + 2) C. (x - 4) D. (x + 4)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Is the binomial a factor of the polynomial function? {{{ f(x) = x^3 + 2x^2 - 16x - 32 }}} Select EACH correct answer. A. (x - 2) B. (x + 2) C. (x - 4) D. (x + 4)       Log On


   



Question 1127826: Is the binomial a factor of the polynomial function?
+f%28x%29+=+x%5E3+%2B+2x%5E2+-+16x+-+32+
Select EACH correct answer.
A. (x - 2)
B. (x + 2)
C. (x - 4)
D. (x + 4)
E. (x + 6)

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Check the possible roots + & - of 1, 2, 4, 8, 16, 32 and see which give remainder 0 in synthetic division.

Answer by ikleyn(52805) About Me  (Show Source):
You can put this solution on YOUR website!
.
The simplest way to solve the problem is to make factoring using the grouping method:


x%5E3+%2B+2x%5E2+-+16x+-+32 = %28x%5E3+-+16x%29 + 2x%5E2+-+32%29 = x%2A%28x%5E2+-+16%29 + 2%2A%28x%5E2+-+16%29 = %28x%5E2-16%29%2A%28x%2B2%29 = %28x-4%29%2A%28x%2B4%29%2A%28x%2B2%29.



The correct answers are  B,  C,  and D.

Solved.