Mathematics 2014 JAMB Past Questions - Question 14: Find the value of k if y -1 is a factor of y³+4y²+ky-6.

Correct Answer

D

Explanation

if y - 1 is a factor ofy3 +4y2 + ky -6, thenf (1) = (1)3 + 4(1) 2+k (1) - 6=0(factor theorem)1+4+k-6 = 0To find the value of k, we need to use the factor theorem. According to the factor theorem, if y - 1 is a factor of y³ + 4y² + ky - 6, then substituting y = 1 into the expression should result in a zero.Let's substitute y = 1 into the expression and solve for k:(1)³ + 4(1)² + k(1) - 6 = 01 + 4 + k - 6 = 05 + k - 6 = 0k - 1 = 0k = 1Therefore, the value of k is 1.5-6+k = 0- 1 + k = 0therefore K = 1