REMAINDER THEOREM PRACTICE QUESTIONS

(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

Solution

(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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