Question

If y3-5y2+7y+m is divided by y +2 the remainder id 50, then find the value of m

Answer 1

Correct Question:

If (y³ - 5y² + 7y + m) is divided by (y + 2) the remainder is 50, then find the value of m.

Solution:

p(y) = y³ - 5y² + 7y + m

The above polynomial is divided by (y + 2)

Applying Remainder Theorem,

(y + 2) = 0

⇒ y = -2

Substitute the value of y in p(y)

p(-2) = (-2)³ - 5(-2)² + 7(-2) + m

Since the remainder is 50,

50 = (-2)³ - 5(-2)² + 7(-2) + m

⇒ 50 = -8 - 5(4) - 14 + m

⇒ 50 = -8 - 20 - 14 + m

⇒ 50 = -42 + m

⇒ m - 42 = 50

⇒ m = 50 + 42

∴ m = 92

Know more:

• Remainder theorem states that if a polynomial p(x) is divided by a binomial (x - a), then the remainder obtained is p(a)