SOLUTION: which of the following is true about the polynomial f(x) = x3 + 9x2 + 24x + 16 ? a. -1 is a zero b. 1 is a zero c. -2 is a zero d. 2i is a zero

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: which of the following is true about the polynomial f(x) = x3 + 9x2 + 24x + 16 ? a. -1 is a zero b. 1 is a zero c. -2 is a zero d. 2i is a zero      Log On


   

Question 371217: which of the following is true about the polynomial f(x) = x3 + 9x2 + 24x + 16 ?
a. -1 is a zero
b. 1 is a zero
c. -2 is a zero
d. 2i is a zero
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+x%5E3+%2B+9x%5E2+%2B+24x+%2B+16+
One of the quickest ways to find a zero is to use Synthetic Division:
-1 |  1   9   24   16
----     -1   -8  -16
      ---------------
      1   8   16    0

Right off the bat we have a zero: -1 And f(x) factors into
f%28x%29+=+%28x%2B1%29%28x%5E2+%2B8x+%2B16%29
The second factor is easily factored giving us:
f%28x%29+=+%28x%2B1%29%28x%2B4%29%28x%2B4%29
We can now see the zeros of f(x): -1 and -4 (twice)