Question

A polynomial of degree 5,P(x) has leading coefficient 9 , and has roots of multiplicity 3 at x=2, multiplicity 1 at x=−3, and multiplicity 1 at x=1. Find a possible formula for P(x). You can leave your answer in factor form. P(x)=

Answer 1

The polynomial P(x) can be represented in factored form as P(x) = 9(x - 2)^3(x + 3)(x - 1).

Step-by-step explanation:

The polynomial P(x) can be represented in factored form as P(x) = 9(x - 2)^3(x + 3)(x - 1).

The factors correspond to the roots of the polynomial. The root x = 2 has a multiplicity of 3, x = -3 and x = 1 have multiplicities of 1 each. The leading coefficient 9 indicates that the polynomial has a degree of 5.

By expanding the factored form, we get P(x) = 9x^5 - 45x^4 + 99x^3 - 99x^2 + 54x - 54.

Learn more about Polynomial roots