Need help solving problem

Question

Give an expression for  with leading coefficient , of degree 3, and having roots  , , and .

My answer was x^3+3x^2-15x-125 which is incorrect

Answer 1

P(x) =k (x - 5)(x - (-4 - 3i))(x - (-4 + 3i))

p(x)=-5(x^3+3x^2-15x-125)

p(x)=-5x^3-15x^2+75x+625

Answer 2

Looks like you found the right polynomial, P(x) that has the roots specified, but P(x) * constant will also have the same roots.

They said that the leading term is -5, so multiply every term by -5.

Take care.

Answer 3

You have half of it correct. Your solution meets the requirements that x=5, x=-4-3i and x=-4+3i.

However, the other requirement is that the leading coefficient equals -5.

To accomplish this, just multiply your answer by -5, giving:

f(x) = -5x^3 -15x^2 +75x+625