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Question
If the polynomial y3 − 5y2 + 7y + m is divided by y + 2 and the remainder is 50 then find the value of m.
Solution
Let p(y) = y3 − 5y2 + 7y + m
When the polynomial is divided by (y + 2), the remainder is 50. This means that the value of the polynomial when y = −2 is 50.
By remainder theorem,
Remainder = p(−2) = 50
∴ (−2)3 − 5 × (−2)2 + 7 (−2) + m = 50
⇒ − 8 − 5 × 4 -14 + m = 50
⇒ − 8 − 20 − 14 + m = 50
⇒ − 42 + m = 50
⇒ m = 50 + 42 = 92
Thus, the value of m is 92.
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