SOLUTION: Write a polynomial function in standard form with zeros at 5, -3, and 1.

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Question 638310: Write a polynomial function in standard form with zeros at 5, -3, and 1.
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
If the zeros 5, -3, 1, we can write the factored expression as
f(x) = (x-5)(x+3)(x-1) = 0
Multiply the first two factors using FOIL, then multiply by the remaining factor:
(x-1)(x^2-2x-15) = x^3 - 2x^2 - 15x - x^2 + 2x + 15
Collecting terms, we get
f(x) = x^3 - 3x^2 - 13x + 15
The graph of the function shows that it gives the correct zeros:
graph%28300%2C300%2C-6%2C6%2C-20%2C20%2Cx%5E3+-+3x%5E2+-+13x+%2B+15%29