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Question
Find the number that must be subtracted from the polynomial 3y3 + y2 – 22y + 15, so that the resulting polynomial is completely divisible by y + 3.
Solution
Let the number to be subtracted from the given polynomial be k.
Let f(y) = 3y3 + y2 – 22y + 15 – k
It is given that f(y) is divisible by (y + 3).
∴ Remainder = f(–3) = 0
3(–3)3 + (–3)2 – 22(–3) + 15 – k = 0
– 81 + 9 + 66 + 15 – k = 0
9 – k = 0
k = 9
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