Question
Factorize the following polynomials: $\left(x^2-2 x+3\right)\left(x^2-2 x+5\right)-35$
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Answer
$\left(x^2-2 x+3\right)\left(x^2-2 x+5\right)-35$
$=(m+3)(m+5)-35 \ldots\left[\text { Putting } x^2-2 x=m\right]$
$=m(m+5)+3(m+5)-35$
$=m^2+5 m+3 m+15-35$
$=m^2+8 m-20$
$=m^2+10 m-2 m-20$
$=m(m+10)-2(m+10)$
$=(m+10)(m-2)$
$=\left(x^2-2 x+10\right)\left(x^2-2 x-2\right) \ldots\left[\right.$ Replacing $\left.m=x^2-2 x\right]$
$\overbrace{10}^{-20}$
$10 \times-2=-20$
$10-2=8$
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