If \(-2x^3 + 6x^2 + 17x\) – 21 is divided by \((x + 1)\), then…

Explanation

Let \(p(x) = -2x^3 + 6x^2 + 17x - 21\)

Using the remainder theorem

Let \(x + 1 = 0\)

∴ \(x = -1\)

Since, \((x + 1)\) divides \(p(x)\), then, remainder will be p(-1)

⇒ p(-1) = -2(-1)\(^3 + 6(-1)^2\) + 17(-1) - 21

∴ p(-1) = -30

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