Question 656066: a. List all possible rational zeros.
b. Use synthetic division to test the possible rational zeros and find an actual zero.
c. Use the quotient from part (b) to find the remaining zeros of the polynomial function.
f(x)= x^3+x^2-4x-4
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! f(x)= x^3+x^2-4x-4
a. List all possible rational zeros.
+-1,+-2,+-4
b. Use synthetic division to test the possible rational zeros and find an actual zero.
testing -1:
-1 | 1 1 -4 -4
-1 0 4
---------------
1 0 -4 0
since, it is evenly divisible, -1 is a root
.
c. Use the quotient from part (b) to find the remaining zeros of the polynomial function.
since -1 is a root, we then have
(x+1)(x^2-4)
factoring right term:
(x+1)(x-2)(x+2)
zeros are then
x = {-2, -1, 2}
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