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What is the remainder, when 4x4 + 10x3 - 20x2 + 90 is divided by (x + 2)?

What is the remainder, when 4x4 + 10x3 - 20x2 + 90 is divided by (x + 2)? Correct Answer -6

If f(x) is divided by (x + a), then the remainder is derived by substituting x = -a in the given expression

For the given problem, the remainder is obtained by substituting x = -2 in the given expression

f(-2) = 4 (-2)4 + 10 (-2)3 - 20 (-2)2 + 90

⇒ (4 × 16) + (10 × -8) - (20 × 4) + 90 = (64 - 80 - 80 + 90) = (154 - 160) = -6

∴ Remainder = -6

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