How do you factor #4x^4+12x^3+9x^2#?

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Answer 1 · 2018-03-16T05:55:49

The factored form of the polynomial is #x^2(2x+3)^2#.

First, factor out #x^2# from all the terms:

#color(white)=4x^4+12x^3+9x^2#

#=color(red)(x^2)*4x^2+color(red)(x^2)*12x+color(red)(x^2)*9#

#=color(red)(x^2)(4x^2+12x+9)#

Next, to factor the inner quadratic, find two numbers that multiply to #9*4# (which is #36#) and add up to #12#.

These two numbers are #6# and #6#. Now, split up the #x# terms into these amounts and factor:

#color(white)=x^2(4x^2+12x+9)#

#=x^2(4x^2+6x+6x+9)#

#=x^2(2x(2x+3)+3(2x+3))#

#=x^2((2x+3)(2x+3))#

#=x^2(2x+3)(2x+3)#

#=x^2(2x+3)^2#

This is the factored form. Hope this helped!