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

Jul 11, 2015

$f \left(x\right) = {x}^{2} {\left(x + 3\right)}^{2}$

#### Explanation:

You can immediately factor out ${x}^{2}$ to get:

$f \left(x\right) = {x}^{4} + 6 {x}^{3} + 9 {x}^{2} = {x}^{2} \left({x}^{2} + 6 x + 9\right)$

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

$f \left(x\right) = {x}^{2} \left({x}^{2} + 6 x + 9\right) = {x}^{2} {\left(x + 3\right)}^{2}$