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The polynomials P(x) = k*x³ + 3x² - 3 and Q(x) = 2x³ - 5x + k leave equal remainders when each is divided by (x - 4). Find k.

1. 2
2. 1
3. 0
4. -1

Correct answer: 1

Solution

By the Remainder Theorem the two remainders are P(4) and Q(4); equating them yields a linear equation in k.

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