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

Question

7296 views around the world

You can reuse this answer
Creative Commons License

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!

How do you factor 4x^4+12x^3+9x^24x^4+12x^3+9x^2?