Question

use remainder theorem to find the remainder when x^3-6x^2-4 is divided by 1-3/2 x

Answer 1

Answer:

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Answer 2

remainder theorem : when any polynomial P(x) is divided by another polynomial g(x) = (x - a), then remainder obtained is P(a).

here P(x) = x³ - 6x² - 4 and g(x) = 1 - (3/2)x

firstly, find value of x at g(x) = 0

g(x) = 1 - (3/2)x = 0

or, x = (2/3)

now from remainder theorem

remainder will be P(2/3)

P(2/3) = (2/3)³ - 6(2/3)² - 4

= (2³/3³) - 6(2²/3²) - 4

= 8/27 - 6 × 4/9 - 4

= 8/27 - 8/3 - 4

= (8 - 72 - 108)/27

= -172/27

hence, answer will be -172/27