SOLUTION: I need help writing a polynomial: Write a polynomial of the smallest degree with roots -8, 9, 10, and -11. Type your answer in standard form, with the equation equal to zero.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need help writing a polynomial: Write a polynomial of the smallest degree with roots -8, 9, 10, and -11. Type your answer in standard form, with the equation equal to zero.       Log On


   

Question 552308: I need help writing a polynomial:
Write a polynomial of the smallest degree with roots -8, 9, 10, and -11. Type your answer in standard form, with the equation equal to zero.
Thanks!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If a polynomial has 9 for a root, (x-9) is a factor of the polynomial.
A polynomial with roots -8, 9, 10, and -11, has as a factor
%28x%2B8%29%28x-9%29%28x-10%29%28x%2B11%29
I don't see an easier way, so I'll grit my teeth and multiply:

That is the simplest polynomial for the answer, and it's in standard form.
Multiplying it by a factor with x to any exponent would make it a polynomial of higher degree. Multiplying it by any number, would give you another acceptable answer, but would be unnecessary extra work.
x%5E4-183x%5E2%2B38x%2B7920=0 is a suitable answer.