SOLUTION: how do i write a polynomial equation with rational coefficients in standard form with the given solutions of 2,3,and 5? I am aware that i need to work backwards starting by making

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: how do i write a polynomial equation with rational coefficients in standard form with the given solutions of 2,3,and 5? I am aware that i need to work backwards starting by making       Log On


   

Question 529810: how do i write a polynomial equation with rational coefficients in standard form with the given solutions of 2,3,and 5? I am aware that i need to work backwards starting by making each solution equal to zero, i think.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You are correct.


x=2, x=3, or x=5


x-2=0, x-3=0, or x-5=0


%28x-2%29%28x-3%29%28x-5%29=0


%28x-2%29%28x%5E2-8x%2B15%29=0


x%28x%5E2-8x%2B15%29-2%28x%5E2-8x%2B15%29=0


x%5E3-8x%5E2%2B15x-2x%5E2%2B16x-30=0


x%5E3-10x%5E2%2B31x-30=0


So the polynomial equation that has the zeros 2, 3, or 5 is x%5E3-10x%5E2%2B31x-30=0


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Jim