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Mathematics

When 2x3 - 9x2 + 10x - p is divided by (x + 1), the remainder is -24. Find the value of p.

Factorisation

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Answer

By remainder theorem, on dividing f(x) by (x - a), the remainder left is f(a).

f(x) = 2x3 - 9x2 + 10x - p

∴ On dividing f(x) by (x + 1) or (x - (-1)), Remainder = f(-1)

∴f(−1)=2(−1)3−9(−1)2+10(−1)−p=−2−9−10−p=−21−p\therefore f(-1) = 2(-1)^3 - 9(-1)^2 + 10(-1) - p \\[0.5em] = -2 - 9 - 10 - p \\[0.5em] = -21 - p

Given, remainder = -24

∴ -21 - p = -24

⇒p=24−21p=3.\Rightarrow p = 24 - 21 \\[0.5em] p = 3.

Hence, the value of p is 3.

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