Question

Write the factored form of the third-degree polynomial

function that has a positive leading coefficient and a
zero at x= -3 with a multiplicity of 3.

Answer 1

`a(x+3)^3, a \\eq 0`

Explanation:

Zeros of a function:

Given a polynomial f(x), this polynomial has roots
`x_(1), x_(2), x_(n)` such that it can be written as:
`a(x - x_(1))*(x - x_(2))*...*(x-x_n)`, in which a is the leading coefficient.

Zero at x= -3 with a multiplicity of 3.

This means that:

`x_1 = x_2 = x_3 = -3`

So

`a(x - (-3))*(x - (-3))*(x-(-3)) = a(x+3)(x+3)(x+3) = a(x+3)^3`

Positive leading coefficient

`a(x+3)^3, a \\eq 0`