Question

If the polynomial y³ – 5y²+ 7y + m is divided by y + 2 and the remainder is 50, then find the value of m.

Answer 1

p(y) = y³ – 5y² + 7y + m

 Divisor = y + 2 

∴ take y = – 2

 ∴ By remainder theorem, 

Remainder = p(- 2) = 50

 P(y) = y³ – 5y ²+ 7y + m 

∴ P(-2) = (- 2)³ – 5(- 2)² + 7(- 2) + m 

∴ 50 = -8 – 5(4) – 14 + m 

∴ 50 = -8 – 20 – 14 + m 

∴ 50 = – 42 + m 

∴ m = 50 + 42 

∴ m = 92