# Solve the following polynomial equation by factoring. 9x^2+24x+16

Solve the following polynomial equation by factoring.
$9{x}^{2}+24x+16$
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Alannej
Step 1
Given:
$9{x}^{2}+24x+16$
Step 2
The given polynomial can be factorized by using factoring perfect square trinomials technique
Here,
$9{x}^{2}={\left(3x\right)}^{2}$
$16={\left(4\right)}^{2}$
24x = 2(3x)(4)
A=3x and B = 4
${A}^{2}+2AB+{B}^{2}={\left(A+B\right)}^{2}$
Step 3
On substituting the values of A and B on the above expression as follows,
$9{x}^{2}+24x+16=\left(3{x}^{2}\right)+2\left(3x\right)\left(4\right)+{\left(4\right)}^{2}$
$={\left(3x+4\right)}^{2}$
Thus the factorization of the given polynomial $9{x}^{2}+24x+16$ is done using factoring perfect square trinomials technique
Jeffrey Jordon