SOLUTION: Please help me graph this problem: Consider the given function. f(x)=x^3+2x^2-x-2 Use the Remainder Theorem to plot all the values of a in the interval [-4, 4] where f(a)

Question 1041569: Please help me graph this problem:

Consider the given function.
f(x)=x^3+2x^2-x-2
Use the Remainder Theorem to plot all the values of a in the interval [-4, 4] where f(a) = 0.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
f(x)=x^3+2x^2-x-2
Remainder theorem says that if one divides by a number a, the remainder is f(a).
We want f(a)=0
synthetic division
2|1===2===-1====-1
=1== 4====7====12; f(2)=12
-2
==1===0===-1===0
-2 is a root, so (x+2) is a factor.
The quotient is the other factor, or x^2-1, which factors into (x+1)(x-1) by difference of squares.
Set those equal to zero, and the roots are -2,-1,and 1, on the interval {-4,4}. Those are all the values of a where f(a)=0.

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