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Find the remainder when 4x3 - 3x + 5 is divided by 2x - 1.

Mathematics

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Here are the solutions to questions 4, 5, 6, 7, 8, and 9.

Part 4

Part a· 2 steps

Find the remainder when 4x3−3x+54x^3 - 3x + 5 is divided by 2x−12x - 1.

  1. Use the Remainder Theorem.

    Let P(x)=4x3−3x+5P(x) = 4x^3 - 3x + 5.
    To find the remainder when P(x)P(x) is divided by 2x−12x-1, we set 2x−1=02x-1=0 and solve for xx:

    2x=12x = 1 x=12x = \frac{1}{2}

  2. Substitute $x = \frac{

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