Question

How do you factor `f(x)= x^4 + 6x^3+9x^2`?

Answer 1

`f(x)=x^2(x+3)^2`

Explanation:

You can immediately factor out `x^2` to get:

`f(x)=x^4+6x^3+9x^2=x^2(x^2+6x+9)`

The term in the brackets can be factors further as it is a quadratic and noting there is a double root at `x=-3`:

`f(x)=x^2(x^2+6x+9)=x^2(x+3)^2`