Check whether p(x) is a multiple of g(x) or not, where p(x) = x³ - x + 1, g(x) = 2 - 3x
Solution:
Given, p(x) = x³ - x + 1
Also, g(x) = 2 - 3x
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
2 - 3x = 0
2 = 3x
x = 2/3
Put x = 2/3 in p(x)
p(2/3) = (2/3)³ - 2/3 + 1
= 8/27 - 2/3 + 1
= (8 - 2(9) + 27)/27
= (8 - 18 + 27)/27
= (-10 + 27)/27
= 17/27
p(x) ≠ 0
This implies 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) = 4x³ + 3x + 1, g(x) = 2x - 3
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Sample Problem 1(i)
Check whether p(x) is a multiple of g(x) or not, where p(x) = x³ - x + 1, g(x) = 2 - 3x
Summary:
p(x) is not a multiple of g(x), where p(x) = x³ - x + 1, g(x) = 2 - 3x since p(x) ≠ 0 when x = 2/3
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