If the polynomial y3 – 5y2 + 7y + m is divided by y + 2 and the rema

1.	If the polynomial y3 – 5y2 + 7y + m is divided by y + 2 and the remainder is 50, then find the value of m.
Answer» p(y) = y³ – 5y² + 7y + m Divisor = y + 2 ∴ take y = – 2 ∴ By remainder theorem, Remainder = p(- 2) = 50 P(y) = y³ – 5y² + 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

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

Answer»

p(y) = y³ – 5y² + 7y + m

Divisor = y + 2

∴ take y = – 2

∴ By remainder theorem,

Remainder = p(- 2) = 50

P(y) = y³ – 5y² + 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