# 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"

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