Check whether p(x) is a multiple of g(x) or not : p(x) = 2x³ - 11x² - 4x + 5, g(x) = 2x + 1
Solution:
Given, p(x) = 2x³ - 11x² - 4x + 5
Also, g(x) = 2x + 1
We have to check whether p(x) is a multiple of g(x) or not.
We know that if p(x) is a multiple of g(x) then g(x) must be divisible by p(x)
Let g(x) = 0
2x + 1 = 0
2x = -1
x = -1/2
Put x = -1/2 in p(x)
p(2) = 2(-1/2)³ - 11(-1/2)² - 4(-1/2) + 5
= -2/8 - 11/4 + 2 + 5
= -1/4 - 11/4 + 7
= (-1 - 11 + 7(4))/4
= (-1 - 11 + 28)/4
= 16/4
= 4
p(x) ≠ 0
Since the remainder is not zero, g(x) is not divisible by p(x)
Therefore, p(x) is not a multiple of g(x).
✦ Try This: Check whether p(x) is a multiple of g(x) or not, where p(x) = x³ + 2x + 8, g(x) = 2x - 3
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 15(ii)
Check whether p(x) is a multiple of g(x) or not : p(x) = 2x³ - 11x² - 4x + 5, g(x) = 2x + 1
Summary:
p(x) is not a multiple of g(x) or not, where p(x) = 2x³ - 11x² - 4x + 5, g(x) = 2x + 1 since p(x) ≠ 0 when x = 2
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