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Factoring

I am trying to factor the polynomial f(x) = 2x^3 - 5x^2 - 4x + 3. I think it is (x-3)(x+1)(x- 1/2). Am I right? (See work below.)

Once I factor f(x), how do I use that to find the answers to the following questions?

a) f(x) = 0
b) f(x+2) = 0
c) f(2x) = 0

This is the work that I used to factor f(x):

3| 2 -5 -4 3
6 3 -3
2 1 -1 0

-1| 2 1 -1 0
-2 1
2 -1 0

1/2| 2 -1 0
1
2 0

So 3, -1, and ½ are zeros.

Solution Preview

Given the polynomial f(x) = 2x^3 - 5x^2 - 4x + 3, find all the solutions if the function is completed.

a) f(x) = 0
b) f(x+2) = 0
c) f(2x) = 0

a) f(x) = 0

You used synthetic division to show that (x + 1), (x - 3), and (x - ½) all go into f(x) ...

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