Show that p - 1 is a factor of p10 - 1 and also of p11 - 1.
Solution:
Given, the polynomials are p10 - 1 and p11 - 1.
Given, the factor g(x) = p - 1.
We have to show that p - 1 is a factor of p10 - 1 and also of p11 - 1.
Let g(x) = 0
p - 1 = 0
p = 1
Let p(x) = p10 - 1
Substitute p = 1 in p(x),
p(1) = (1)10 - 1
= 1 - 1
= 0
p(1) = 0
Since p(x) = 0 when x = 1, x - 1 is the factor of p(x).
Let q(x) = p11 - 1
Substitute p = 1 in p(x),
q(1) = (1)11 - 1
= 1 - 1
= 0
q(1) = 0
Since q(x) = 0 when x = 1, x - 1 is the factor of q(x).
Therefore, x - 1 is a factor of p(x) and q(x).
✦ Try This: Show that p + 1 is a factor of p10 + 1 and also of p12 + 1.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 18
Show that p - 1 is a factor of p10 - 1 and also of p11 - 1
Summary:
It is shown that p - 1 is a factor of p10 - 1 and also of p11 - 1 since p(x) and q(x) is equal to zero when x = 1
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