Find the remainder on dividing (5x³ + 4x² − 10x + 1) by (2x - 4).
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Correct answer: B
Explanation
Given:
P(x) = 5x³ + 4x² − 10x + 1
Divisor = 2x − 4
By the formula:
Remainder Theorem
If the divisor is 2x − 4, then substituting x = 2 gives the remainder:
P(2) = 5(2³) + 4(2²) − 10(2) + 1
= 5(8) + 4(4) − 20 + 1
= 40 + 16 − 20 + 1
= 37