WAEC 2014 Mathematics · Question 34

If (x - a) is a factor pf bx - ax + x2, find the other factor.

Options

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

Answer: A. (x + b)

Explanation written with AI and checked against the answer key

Analyze the question: We have the expression bx − ax + x², and we're told (x − a) is a factor. We need the other factor. Concept: Rearrange and factorise by grouping or by polynomial division. Solution: Write the expression in order of powers of x: x² − ax + bx Factor out x from every term: x(x − a + b) This does not contain (x − a) as a factor in general, so let's check whether the question was typed correctly. Test with x = a (the factor theorem): substituting x = a gives a² − a·a + b·a = ab This is not zero unless a = 0 or b = 0. So (x − a) is not actually a factor of bx − ax + x² as written. Likely intended question: The original is probably "bx − ax + x²" with a typo, for example bx − ab + x² − ax... Let's find the version that fits the options. If the expression were x² − ax + bx − ab = x(x − a) + b(x − a) = (x − a)(x + b) then the other factor is (x + b), which is option A. Important note: As literally typed (bx − ax + x²), (x − a) is not a factor, so the question appears to be missing the term −ab. With that term included, the working above gives (x − a)(x + b). Answer: A. (x + b) Tip: When told a binomial is a factor, use the factor theorem: put x = a into the expression, and it must give 0. This quickly shows whether a question has a typo and helps you check your answer.

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