# REMAINDER THEOREM PRACTICE QUESTIONS

## About "Remainder Theorem Practice Questions"

Remainder Theorem Practice Questions :

Here we are going to see some practice problems using the concept of remainder theorem.

## Remainder Theorem Practice Questions - Examples

(1)  Check whether p(x) is a multiple of g(x) or not .

p(x) = x3 - 5x2 + 4x - 3 ; g(x) = x – 2

Solution

(2)  By remainder theorem, find the remainder when, p(x) is divided by g(x) where,

(i)  p(x) = x3 - 2x2 - 4x - 1 and g(x)  =  x + 1

(ii)  p(x)  =  4x3 - 12x2 + 14x - 3 and g(x)  =  2x - 1

(iii)  p(x)  =  x3 - 3x2 + 4x + 50 and g(x)  =  x - 3

(3)  Find the remainder when 3x3 - 4x2 + 7x - 5 is divided by (x+3).              Solution

(4)  What is the remainder when x2018 + 2018 is divided by x – 1               Solution

(5)  For what value of k is the polynomial p(x)  =  2x3 - kx2 + 3x + 10 exactly divisible by (x – 2)      Solution

(6)  If two polynomials 2x3 + ax2 + 4x – 12 and x3 + x2 –2x+ a leave the same remainder when divided by (x – 3), find the value of a and also find the remainder    Solution

(7)  Determine whether (x -1) is a factor of the following polynomials:

(i) x3 + 5x2 - 10x + 4

(ii)  x4 + 5x2 - 5x + 1               Solution

(8)  Using factor theorem, show that (x - 5) is a factor of the polynomial 2x3 - 5x2 - 28x + 15

(9)  Determine the value of m, if (x + 3) is a factor of x3 - 3x2 - mx + 24

(10)  If both (x -2) and (x - (1/2)) are the factors of ax2 + 5x + b, then show that a  =  b.

(11)  If (x - 1) divides the polynomial kx3 - 2x2 + 25x  - 26 without remainder, then find the value of k .

(12)  Check if (x + 2) and (x - 4) are the sides of a rectangle whose area is x2 - 2x - 8 by using factor theorem.       Solution After having gone through the stuff given above, we hope that the students would have understood, "Remainder Theorem Practice Questions"

Apart from the stuff given in this section if you need any other stuff in math, please use our google custom search here.