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Polynomials — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsPolynomials2 Marks
Question
Factorize the following polynomials: $(x-3)(x-4) 2(x-5)-6$
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Answer

$(x-3)(x-4) 2(x-5)-6$
$=(x-3)(x-5)(x-4)^2-6$
$=\left(x^2-5 x-3 x+15\right)\left(x^2-8 x+16\right)-6$
$=\left(x^2-8 x+15\right)\left(x^2-8 x+16\right)-6$
$=(m+15)(m+16)-6 \ldots\left[\text { Putting } x^2-8 x=m\right]$
$=m(m+16)+15(m+16)-6$
$=m^2+16 m+15 m+240-6$
$=m^2+31 m+234$
$=m^2+18 m+13 m+234$
$=m(m+18)+13(m+18)$
$=(m+18)(m+13)$
$=\left(x^2-8 x+18\right)\left(x^2-8 x+13\right) \ldots\left[\text { Replacing } m=x^2-8 x\right]$

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