SOLUTION: Write a polynomial function that has the zeros 4, 2, and 1 and has a leading coefficient of 1. Then graph the function.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write a polynomial function that has the zeros 4, 2, and 1 and has a leading coefficient of 1. Then graph the function.      Log On


   

Question 825386: Write a polynomial function that has the zeros 4, 2, and 1 and has a leading coefficient of 1. Then graph the function.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
A general form for a polynomial in factored form is:
f%28x%29+=+a%28x-z%5B1%5D%29%28x-z%5B2%5D%29...
where "a" is the leading coefficient and the z's are the zeros of the polynomial. Using the given leading coefficient and the given zeros we get:
f%28x%29+=+%281%29%28x-4%29%28x-2%29%28x-1%29

All that is left is to multiply this out:
f%28x%29+=+%28x-4%29%28x-2%29%28x-1%29
f%28x%29+=+%28x%5E2-6x%2B8%29%28x-1%29
f%28x%29+=+x%5E3-7x%5E2%2B11x-8