NECO 2005 Mathematics · Question 18

For what value(s) of x is the expression (x2 + 15x + 50) ÷ (x - 5) not defined

Options

A.-5, -10
B.-10
C.-5
D.5
E.10, 5

Answer: D. 5

Explanation written with AI and checked against the answer key

Analyze the question A fraction (or division) is not defined when its denominator is zero. So we need the value of x that makes the divisor x − 5 equal to zero. Concept Division by zero is undefined. For (x² + 15x + 50) ÷ (x − 5), the expression is undefined when x − 5 = 0. Solution Set the denominator equal to zero: x − 5 = 0 x = 5 Note: the numerator factorises as x² + 15x + 50 = (x + 5)(x + 10). Its roots, −5 and −10, make the whole expression equal to zero, not undefined. This is the trap in options A, B and C. Also, the numerator does not contain a factor (x − 5), so nothing cancels, and x = 5 really is a point where the expression is undefined. Answer The expression is not defined when x = 5, which is option D. Tip "Not defined" means look only at the denominator. Set the denominator to zero and solve. Zeros of the numerator are where the expression equals 0, which is a different question.

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