SOLUTION: Write the equation of the polynomial function with the given zeros: 3,4,-2

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Question 286542: Write the equation of the polynomial function with the given zeros:
3,4,-2

Found 3 solutions by jim_thompson5910, richwmiller, Fombitz:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: if 3, 4, and -2 are zeros, then x=3, x=4 or x=-2. Get all of the nonzero terms to the left side to get x-3=0, x-4=0, or x+2=0. Use the zero product property to then get %28x-3%29%28x-4%29%28x%2B2%29=0. From here, just FOIL and expand.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
(x-3)*(x-4)*(x+2)=0
foil these factors
(x-3)*(x-4)=
to get x^2-7x+12
Multiply each part by x and by 2 and add them to get
x^3-5x^2-2x+24=0

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since they are the zeros, then the factors are
%28x-3%29
%28x-4%29
%28x%2B2%29
The simplest polynomial would be the product of these three factors,
f%28x%29=%28x-3%29%28x-4%29%28x%2B2%29
f%28x%29=%28x%5E2-7x%2B12%29%28x%2B2%29
f%28x%29=x%5E3-7x%5E2%2B12x%2B2x%5E2-14x%2B24
f%28x%29=x%5E3-5x%5E2-2x%2B24
I leave it to you to verify that 3, 4, and -2 are still zeros for f(x).