JAMB - Mathematics (2023 - No. 35)
If \(-2x^3 + 6x^2 + 17x\) - 21 is divided by \((x + 1)\), then the remainder is
32
30
-30
-32
स्पष्टीकरण
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
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