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The polynomial P(x) = 7x⁴ + 8x² - 3x + lambda gives a remainder of 3 when divided by (x + 1). Find the value of lambda.

1. 12
2. 15
3. -15
4. -12

Correct answer: -15

Solution

By the Remainder Theorem, P(-1) = 3. P(-1) = 7(1) + 8(1) + 3 + lambda = 18 + lambda = 3, giving lambda = -15.

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