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Factorize each of the following polynomials:$4x^3 + 20x^2 + 33x + 18$ given that $2x + 3$ is a factor.
Given:
Given expression is $4x^3 + 20x^2 + 33x + 18$ and $2x + 3$ is a factor.
To do:
We have to factorize the given polynomial.
Solution:
Let $f(x)=4x^3 + 20x^2 + 33x + 18$
Dividing $f(x)$ by $2x+3$, we get,
$2x + 3$) $4x ^ { 3 } + 20 x ^ { 2 } + 3 3 x + 18$ ( $2x ^ { 2 } + 7 x +6$
$4x^3+6x^2$
------------------------------------
$14x^2+33x+18$
$14x^2+21x$
--------------------------
$12x+18$
$12x+18$
------------------
0
$f(x)=(2x+3)(2x^{2}+7 x+6)$
$=(2x+3)(2x^{2}+4 x+3x+6)$
$=(2x+3)[2x(x+2)+3(x+2)]$
$=(2x+3)(2x+3)(x+2)$
Hence, $4x^3 + 20x^2 + 33x + 18=(2x+3)(2x+3)(x+2)$. 
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