Mathematics 2018 JAMB Past Questions - Question 6: find the value of u if y -1 is a factor of y³ + 4y² + 4y- 6

Correct Answer

D

Explanation

(1) 3 + 4 (1) 2 + 1k -6 = 01+ 4 + K - 6 = 0k -1 = 0 =k =1To find the value of \( u \) if \( y - 1 \) is a factor of \( y^3 + 4y^2 + 4y - 6 \), we can use polynomial long division or synthetic division to divide \( y^3 + 4y^2 + 4y - 6 \) by \( y - 1 \).Performing the division, we get:\[\begin{array}{c|cccc}& y^2 & +5y & +9 \\\hliney-1 & y^3 & +4y^2 & +4y & -6 \\& -(y^3 & -y^2) & & \\\hline& & 5y^2 & +4y & \\& & -(5y^2 & -5y) & \\\hline& & & 9y & -6 \\& & & -(9y & -9) \\\hline& & & & 3\end{array}\]So, after performing the division, we get a remainder of 3. According to the Remainder Theorem, the remainder obtained when a polynomial is divided by \( y - u \) is the value of the polynomial at \( y = u \). Therefore, the value of \( u \) is 3.