JAMB 2014 Mathematics · Question 11

Find the value of k if y - 1 is a factor of y3 + 4y2 + ky - 6

Options

A.-6
B.-4
C.O
D.1

Answer: D. 1

Explanation written with AI and checked against the answer key

Analyze the question: We are told (y − 1) is a factor of y³ + 4y² + ky − 6. We need k. Concept (Factor Theorem): If (y − a) is a factor of a polynomial P(y), then P(a) = 0. Solution: Here a = 1, so P(1) = 0: P(1) = (1)³ + 4(1)² + k(1) − 6 = 1 + 4 + k − 6 = k − 1 Set equal to zero: k − 1 = 0, so k = 1 Check: With k = 1, P(y) = y³ + 4y² + y − 6. P(1) = 1 + 4 + 1 − 6 = 0 ✓. Tip: For "(y − a) is a factor" questions, just substitute y = a and set the expression equal to 0. Remember the sign: (y − 1) gives y = +1, while (y + 1) would give y = −1.

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