waecmaths question:
Given that $(x+2)({{x}^{2}}-3x+2)+2(x+2)(x-1)=(x+2)M$, find M
Option A:
${{(x+2)}^{2}}$
Option B:
$x(x+2)$
Option C:
${{x}^{2}}+2$
Option D:
${{x}^{2}}-x$
waecmaths solution:
$\begin{align} & (x+2)({{x}^{2}}-3x+2)+2(x+2)(x-1)=(x+2)M \\ & (x+2)(x-1)(x-2)+2(x+2)(x-1)=(x+2)M \\ & (x+2)(x-1)[(x-2)+2]=(x+2)M \\ & (x+2)(x-1)x=(x+2)M \\ & Divide\text{ both side }(x+2) \\ & M=x(x-1)={{x}^{2}}-x \\\end{align}$
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