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WAEC Mathematics 2013 Paper

Question : 33

Total: 48

Given that (x + 2)(x² - 3x + 2) + 2(x + 2)(x - 1) = (x + 2) M, find M

Solution:

Concept:

Factor out the common term

(x + 2)

from both terms on the left-hand side, then simplify to isolate

M

Explanation:

Start with the given equation:

(x + 2)(x^2 - 3x + 2) + 2(x + 2)(x - 1) = (x + 2)M

Since

(x + 2)

appears in both terms on the left, factor it out:

(x + 2)\left[(x^2 - 3x + 2) + 2(x - 1)\right] = (x + 2)M

Divide both sides by

(x + 2)

, assuming

x + 2 \neq 0

(x^2 - 3x + 2) + 2(x - 1) = M

Expand the second group:

x^2 - 3x + 2 + 2x - 2 = M

Combine like terms:

x^2 - 3x + 2x + 2 - 2 = M

Simplify:

x^2 - x = M

Therefore, the correct expression for

M

x^2 - x

Answer:

M = x^2 - x

This corresponds to Option D.

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