SOLUTION: PLEASE HELP ME WITH THIS PROBLEM : Find a polynominal with leading coefficient 1 and degree 3 that has -1, 1, and 3 as roots.

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Question 54411This question is from textbook algebra and trigonometry
: PLEASE HELP ME WITH THIS PROBLEM :
Find a polynominal with leading coefficient 1 and degree 3 that has -1, 1, and 3 as roots.
 This question is from textbook algebra and trigonometry

Found 2 solutions by Nate, funmath:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
Root Determination: (x - root)
Root of -1 ~> (x + 1)
Root of 1 ~> (x - 1)
Root of 3 ~> (x - 3)
(x + 1)(x - 1)(x - 3)
(x^2 - 1)(x - 3)
x^3 - x - 3x^2 + 3
f(x) = x^3 - 3x^2 - x + 3
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E3-3x%5E2-x%2B3%29

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
The roots are -1,1,and 3 and the degree is 3.
(x=1)(x-1)(x-3)=0 when x=-1,1, or 3
Expand:
f%28x%29=%28x%2B1%29%28x-1%29%28x-3%29
f%28x%29=%28x%5E2-x%2Bx-1%29%28x-3%29
f%28x%29=%28x%5E2-1%29%28x-3%29
f%28x%29=x%5E2%28x%29%2Bx%5E2%28-3%29-1%28x%29-1%28-3%29
highlight%28f%28x%29=x%5E3-3x%5E2-x%2B3%29
Happy Calculating!!!