college algebra

Question

Construct a polynomial function with the following properties: fifth degree, 3 is a zero of multiplicity 3, −2 is the only other zero, leading coefficient is 4.

Answer 1

(x-3)^3 times (x+2)^2

there has to be as many factors as the degree, so -2 must have multiplicity 2

then you want a 4 in front

4(x-3)³(x+2)²

expand, multiply it out and the leading coefficient of the 5th degree term is 4

it's a little tedious, but here's part of it

4(x^2 -6x + 9)(x-3)(x^2+4x+4)

1st term is 4x^5, constant term is -3(9)(4) = -108, also an x^4, x^3, x^2 and x terms with coefficients