SOLUTION: The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x=2 and x=0, and a root of multiplicity 1 at x=−3. Find a possible formula for

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x=2 and x=0, and a root of multiplicity 1 at x=−3. Find a possible formula for       Log On


   

Question 1110665: The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x=2 and x=0, and a root of multiplicity 1 at x=−3.
Find a possible formula for P(x).
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If P%28x%29 has a root of multiplicity 1 at x=-3%29 ,
there must be a %28x-%28-3%29%29=%28x%2B3%29 factor in its factored form.
If a polynomial has a root x=a with multiplicity 2,
%28x-a%29%5E2 must appear in that polynomial's factored form,
so highlight%28P%28x%29=x%5E2%28x-2%29%5E2%28x%2B3%29%29
is an expression for the polynomial in this problem.
It is a polynomial of degree 5, and its leading coefficient is 1.
For another form, we multiply
P%28x%29=x%5E2%28x%5E2-4x%2B4%29%28x%2B3%29
P%28x%29=x%5E2%28x%5E3-4x%5E2%2B4x%2B3x%5E2-12x%2B12%29
P%28x%29=x%5E2%28x%5E3-x%5E2-8x%2B12%29
highlight%28P%28x%29=x%5E5-x%5E4-8x%5E3%2B12%5E2%29