NECO 2005 Mathematics · Question 27

If (x - a) is a factor of bx - ax + x2 - ab, what is the other factor?

Options

A.(x + b)
B.(b - a)
C.(x - a)
D.(a + b)
E.(a - b)

Answer: A. (x + b)

Explanation written with AI and checked against the answer key

Analyze the question: We are told (x - a) is a factor of the expression bx - ax + x² - ab, and we must find the other factor. Concept: Rearrange the expression and factorise by grouping, or use long division. Solution: Expression: bx - ax + x² - ab Rewrite in order: x² - ax + bx - ab Group the terms: (x² - ax) + (bx - ab) Factor each group: x(x - a) + b(x - a) Take out the common factor (x - a): (x - a)(x + b) So the other factor is (x + b). Check by expanding: (x - a)(x + b) = x² + bx - ax - ab, which matches the original expression. Answer: Option A, (x + b). Tip: When an expression has four terms, first arrange them by powers of x, then group in pairs. If the brackets that appear in both groups match, you have factorised correctly. If they don't match, try regrouping.

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