SOLUTION: I can't seem to solve... Find a polynomial function of degree 4 with minus−1 as a zero of multiplicity​ 3, 0 as a zero of multiplicity 1

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Question 1004102: I can't seem to solve...
Find a polynomial function of degree 4 with minus−1 as a zero of multiplicity​ 3, 0 as a zero of multiplicity 1
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

Find a polynomial function of
degree 4 with
x%5B1%5D=-1 as a zero of multiplicity 3,
x%5B2%5D=0 as a zero of multiplicity 1
use zero product formula:
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B1%5D%29%28x-x%5B1%5D%29%28x-x%5B2%5D%29
f%28x%29=%28x-%28-1%29%29%28x-%28-1%29%29%28x-%28-1%29%29%28x-0%29
f%28x%29=%28x%2B1%29%28x%2B1%29%28x%2B1%29%28x%29
f%28x%29=%28x%5E2%2Bx%2Bx%2B1%29%28x%2B1%29%28x%29
f%28x%29=%28x%5E2%2B2x%2B1%29%28x%5E2%2Bx%29
f%28x%29=x%5E4%2B2x%5E3%2Bx%5E2%2Bx%5E3%2B2x%5E2%2Bx
f%28x%29=x%5E4%2B3x%5E3%2B3x%5E2%2Bx

+graph%28+600%2C+600%2C+-5%2C5%2C+-5%2C+10%2C+x%5E4%2B3x%5E3%2B3x%5E2%2Bx%29+