Remainder Theorem Practice Questions :
Here we are going to see some practice problems using the concept of remainder theorem.
(1) Check whether p(x) is a multiple of g(x) or not .
p(x) = x3 - 5x2 + 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) = 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 Solution
(9) Determine the value of m, if (x + 3) is a factor of x3 - 3x2 - mx + 24 Solution
(10) If both (x -2) and (x - (1/2)) are the factors of ax2 + 5x + b, then show that a = b. Solution
(11) If (x - 1) divides the polynomial kx3 - 2x2 + 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 x2 - 2x - 8 by using factor theorem. Solution
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