Question
Factorize the following polynomials: $(x-5)^2-(5 x-25)-24$
✓
Answer
$(x-5)^2-(5 x-25)-24$
$=(x-5)^2-(5 x-25)-24$
$=(x-5)^2-5(x-5)-24$
$=m^2-5 m-24 \ldots[\text { Putting } x-5=m \text { ] }$
$=m^2-8 m+3 m-24$
$=m(m-8)+3(m-8)$
$=(m-8)(m+3)$
$=(x-5-8)(x-5+3) \ldots \text { [Replacing } m=x-5]$
$=(x-13)(x-2)$
$=(x-5)^2-(5 x-25)-24$
$=(x-5)^2-5(x-5)-24$
$=m^2-5 m-24 \ldots[\text { Putting } x-5=m \text { ] }$
$=m^2-8 m+3 m-24$
$=m(m-8)+3(m-8)$
$=(m-8)(m+3)$
$=(x-5-8)(x-5+3) \ldots \text { [Replacing } m=x-5]$
$=(x-13)(x-2)$
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