**Remainder Theorem Practice Questions :**

In this section, we are going to see some practice questions on remainder theorem.

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

p(x) = x^{3} - 5x^{2} + 4x - 3 ; g(x) = x – 2

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

(i) p(x) = x^{3} - 2x^{2} - 4x - 1 and g(x) = x + 1

(ii) p(x) = 4x^{3} - 12x^{2} + 14x - 3 and g(x) = 2x - 1

(iii) p(x) = x^{3} - 3x^{2} + 4x + 50 and g(x) = x - 3

(3) Find the remainder when 3x^{3} - 4x^{2} + 7x - 5 is divided by (x+3). Solution

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

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

(6) If two polynomials 2x^{3} + ax^{2} + 4x – 12 and x^{3} + x^{2} –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) x^{3} + 5x^{2} - 10x + 4

(ii) x^{4} + 5x^{2} - 5x + 1 Solution

(8) Using factor theorem, show that (x - 5) is a factor of the polynomial 2x^{3} - 5x^{2} - 28x + 15 Solution

(9) Determine the value of m, if (x + 3) is a factor of x^{3} - 3x^{2} - mx + 24 Solution

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

(11) If (x - 1) divides the polynomial kx^{3} - 2x^{2} + 25x - 26 without remainder, then find the value of k . Solution

(12) Check if (x + 2) and (x - 4) are the sides of a rectangle whose area is x^{2} - 2x - 8 by using factor theorem. Solution

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