SOLUTION: how do i turn -5, 4, and 6 into polynomial funtions with rational coeffients in standard form?

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Question 152793: how do i turn -5, 4, and 6 into polynomial funtions with rational coeffients in standard form?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Since -5, 4, and 6 are given zeros this means that:


x=-5, x=4, and x=6


Get all terms to the left side in each case


x%2B5=0, x-4=0, and x-6=0



%28x%2B5%29%28x-4%29%28x-6%29=0 Now use the zero product property in reverse to join the factors.


%28x%2B5%29%28x%5E2-10x%2B24%29=0 FOIL


x%28x%5E2-10x%2B24%29%2B5%28x%5E2-10x%2B24%29=0 Distribute


x%5E3-10x%5E2%2B24x%2B5x%5E2-50x%2B120=0 Distribute again


x%5E3-5x%5E2-26x%2B120=0 Combine like terms


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Answer:

So the polynomial with roots of -5, 4, and 6 is

y=x%5E3-5x%5E2-26x%2B120



Notice how if we graph y=x%5E3-5x%5E2-26x%2B120, we can visually verify our answer

+graph%28+500%2C+500%2C+-10%2C+10%2C+-50%2C+150%2C+x%5E3-5%2Ax%5E2-26%2Ax%2B120+%29+ Graph of y=x%5E3-5%2Ax%5E2-26%2Ax%2B120 with roots of x=-5, x=4, and x=6