Question

Khan Academy

Answer 1

Answer:

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

Step-by-step 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: $f(x)=(x+3)(x-2)(x+6)$