Question

Khan Academy

Factor using polynomial division
The polynomial p(x) = x3 + 7x2 – 36 has a known factor of (x + 3).
Rewrite p(x) as a product of linear factors.
p(2) =

Answer 1

Rewriting p(x) as a product of linear factors:
`\mathbf{f(x)=(x+3)(x-2)(x+6)}`

Explanation:

The polynomial
`p(x) = x^3 + 7x^2 - 36` has a known factor of
`(x + 3)`

We need to find other factors.

First we find quotient of
`p(x) = x^3 + 7x^2 - 36` divided by
`(x + 3)`

The division is shown in image attached.

The quotient is:
`x^2+4x-12`

Now, factoring the quotient
`x^2+4x-12`

`x^2+4x-12\\=x^2+6x-2x-12\\=x(x+6)-2(x+6)\\=(x-2)(x+6)`

The other two factors are (x-2)(x+6)

So, Rewriting p(x) as a product of linear factors:
`f(x)=(x+3)(x-2)(x+6)`