When p(x) = 4x3 – 12x2 + 11x – 5 is divided by (2x

Foundation

Mathematics Foundation

Remainder Theorem

Question

When p(x) = 4x³ – 12x² + 11x – 5 is divided by (2x – 1), the remainder is

–2

–5

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To find the remainder when polynomial p(x) is divided by (2x - 1), we use the Remainder Theorem. The theorem states that the remainder is equal to p(a), where (x - a) is the divisor. For (2x - 1), we set 2x - 1 = 0, so x = 1/2.

We compute p(1/2):

$p (\frac{1}{2}) = 4 {(\frac{1}{2})}^{3} - 12 {(\frac{1}{2})}^{2} + 11 (\frac{1}{2}) - 5 = 4 (\frac{1}{8}) - 12 (\frac{1}{4}) + \frac{11}{2} - 5 = \frac{1}{2} - 3 + \frac{11}{2} - 5 = (\frac{1}{2} + \frac{11}{2}) - 8 = 6 - 8 = - 2$

Final answer: –2