Can I get factored form please

Question

Find a polynomial f(x) of degree 3 that has the following zeros -8, (multiplicity 2), 9

Answer 1

The zero "-8" has an associated factor of (x + 8) and the zero "9" has an associated factor of (x - 9).

Since -8 has a multiplicity of 2, there are two "(x + 8)" factors.

So the polynomial will be f(x) = (x + 8)(x + 8)(x - 9). To multiply this out, just multiply two of these together and then multiply the third by the result.

Answer 2

Roots are: -8, -8, 9

Polynomial formula is f(x) = (x-a) * (x-b) * (x-c) where a,b & c are factors or roots of the polynomial.

ANSWER:

Factored Form:

f(x) = (x+8)(x+8)(x-9)

FOIL the first two to get:

f(x) = (x² + 16x + 64) (x-9)

Multiply out to get:

f(x) = (x³ + 16x² + 64x) + (-9x² - (16*9)x - (64*9))

f(x) = (x³ + 16x² + 64x) + (-9x² - 144x - 576)

f(x) = x³ + 7x² - 80x - 576

ANSWER:

Expanded Form:

f(x) = x³ + 7x² - 80x - 576