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

1 Answer

Adrian D. · George C.

Jul 11, 2015

#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#

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