By Remainder Theorem Find The Remainder, When P(x) Is Divided By ...

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By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x³ - 6x² + 2x - 4, g(x) = 1 - 3x/2

Solution:

Given, p(x) = x³ - 6x² + 2x - 4

g(x) = 1 - 3x/2

We have to find the remainder by remainder theorem when p(x) is divided by g(x).

The remainder theorem states that when a polynomial f(x) is divided by a linear polynomial , x - a, the remainder of that division will be equivalent to f(a).

Let g(x) = 0

1 - 3x/2 = 0

3x/2 = 1

x = 2/3

Substitute x = 2/3 in p(x) to get the remainder,

p(3) = (2/3)³ - 6(2/3)² + 2(2/3) - 4

= 8/27 - 6(4/9) + 4/3 - 4

= (8 - 24(3) + 4(9) - 4(27))/27

= (8 - 72 + 36 - 108)/27

= -136/27

Therefore, the remainder is -136/27.

✦ Try This: By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x³ + 6x² - 10x - 3, g(x) = x + 2

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2

NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 14(iv)