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

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Answer 1 · 2015-07-11T21:18:08

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

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 $x=-3$ :

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

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