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Question: I Need Help With Writing a Polynomial Function Equation (College Algebra)
The question asks"Find a degree 4 polynomial having zeros −5, −2, 4 and 5 and the leading coefficient is equal to −2. "P(x)=??? I need help finding the factored form, not simplified.I have tried 3 different ways to solve this problem but it keeps telling me I get the answer incorrect. Thank you!

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Answered By:

Victoria V.
Math Teacher: 20 Yrs Teaching/Tutoring Calculus, PreCalc, Alg 2, Trig
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Written Explanation:

Each zero was once a factor. x = -5 Add 5 to both sides and get the factor (x+5)=0x = -2 Add 2 to both sides and get the factor (x+2)=0x = 4 Add -4 to both sides and get the factor (x-4)=0x = 5 Add -5 to both sides and get the factor (x-5)=0f(x) = A(x+5)(x+2)(x-4)(x-5)And since the leading coefficient is -2, this is what goes in place of "A" in the f(x)f(x) = -2 (x+5) (x+2) (x-4) (x-5)Here is graph of our f(x) - ignore the y-values, I had to shrink it to get it to fit, but pay attention to the zeros, the points where it crosses the x-axis. Notice they are the zeros given in the question. So we have the correct function.
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