SOLUTION: Find the polynomial P(x) of lowest degree that has the zeros, 5,-5,1,-1. Answer: I know I have to set everything to 0. x-5=0 x+5=0 x-1=0 x+1=0 (x-5)(x+5)(x-1)(x+1)=0 Now

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the polynomial P(x) of lowest degree that has the zeros, 5,-5,1,-1. Answer: I know I have to set everything to 0. x-5=0 x+5=0 x-1=0 x+1=0 (x-5)(x+5)(x-1)(x+1)=0 Now       Log On


   

Question 431702: Find the polynomial P(x) of lowest degree that has the zeros, 5,-5,1,-1.
Answer: I know I have to set everything to 0.
x-5=0
x+5=0
x-1=0
x+1=0
(x-5)(x+5)(x-1)(x+1)=0
Now from there I don't know how to continue.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
(x-5)(x+5)(x-1)(x+1)=0
is mostly right. It should be:
P(x) = (x-5)(x+5)(x-1)(x+1)

All that is left is to multiply out the right side. I'd suggest mulitplying the first two factors and the last two factors first. For these we can use the %28a%2Bb%29%28a-b%29+=+a%5E2-b%5E2 pattern to multiply quickly:
P%28x%29+=+%28x%5E2+-+5%5E2%29%28x%5E2+-+1%5E2%29
or
P%28x%29+=+%28x%5E2+-+25%29%28x%5E2+-+1%29
Now just use FOIL to multiply the remaining factors.