SOLUTION: Factor to find all the real zeros of P(x)= 2x^3+5x^2-12x

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Question 376787: Factor to find all the real zeros of P(x)= 2x^3+5x^2-12x
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
P%28x%29=+2x%5E3%2B5x%5E2-12x
When factoring always start with the Greatest Common Factor (GCF), The GCF of F(x) is x. Factoring out x we get:
P%28x%29=+x%282x%5E2%2B5x-12%29
The second factor is a quadratic trinomial which factors as follows:
P%28x%29=+x%282x-3%29%28x%2B4%29

(Note: If you have trouble factoring trinomials like 2x%5E2%2B5x-12 then use the Quadratic Formula. You will get -4 and 3/2 as answers from the Quadratic Formula. This makes (x- (-4)) (or (x+4)) and (2x - 3) factors. Note where the numerator and denominator of 3/2 ended up in (2x/3).)

P(x) is now fully factored. And from the factors we can find the zeros by setting each factor equal to zero and then solving for x:
x = 0 or 2x-3 = 0 or x+4 = 0
The first equation is already solved for x. Solving the other tow we get:
x = 0 or x = 3/2 or x = -4
These are the three zeros of P(x).