Question 49

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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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