SOLUTION: Write the expression of a polynomial function with the following properties: Zeros: -2, m=2 3, m=1 1, m=2 0, m=1 Passes through (-1, 32)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write the expression of a polynomial function with the following properties: Zeros: -2, m=2 3, m=1 1, m=2 0, m=1 Passes through (-1, 32)      Log On


   

Question 1173283: Write the expression of a polynomial function with the following properties:
Zeros:
-2, m=2
3, m=1
1, m=2
0, m=1
Passes through (-1, 32)
Answer by greenestamps(13200) About Me  (Show Source):
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Write the expression of a polynomial function with the following properties:
Zeros:

-2, m=2 --> two factors of (x+2)
3, m=1 --> one factor of (x-3)
1, m=2 --> two factors of (x-1)
0, m=1 --> one factor of (x)

p%28x%29+=+a%28%28x%2B2%29%5E2%29%28x-3%29%28%28x-1%29%5E2%29%28x%29

Passes through (-1, 32)

Substitute x=-1 to find coefficient a

32+=+a%281%5E2%29%28-4%29%28%28-2%29%5E2%29%28-1%29
32+=+16a
a+=+2

The polynomial is

p%28x%29+=+2%28%28x%2B2%29%5E2%29%28x-3%29%28%28x-1%29%5E2%29%28x%29