Show that p - 1 is a factor of p10 -1 and also of p11 -1. – InterviewSolution

InterviewSolution

1.

Show that p - 1 is a factor of p10 -1 and also of p11 -1.

Answer»

Let g (p) = p¹⁰ -1

and h(p) = p¹¹ -1.

On putting p=1 in Eq. (i), we get

g(1)=1¹⁰-1 = 1-1=0

Hence, p-1 is a factor of g(p).

Again, putting p = 1 in Eq. (ii), we get

h(1) = (1)¹¹ - 1 = 1 - 1 = 0

Hence, p -1 is a factor of h(p)

Discussion

No Comment Found

Related InterviewSolutions

Find a quadratic polynomial, the sum and product of whose zeroes are -8/3 and 4/3, respectively. Also find its zeroes.
Find a quadratic polynomial, the sum and product of whose zeroes are -3/2√5 and -1/2, respectively. Also find its zeroes.
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, -7, -14 respectively.
If the zeroes of the cubic polynomial x3 - 6x2 + 3x + 10 are of the form a, a + b and a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.
Given that zeroes of cubic polynomial `x^(3)-6x^(2)+3x +10` are of the form a,a+b,a+2b for some real numbers a and b, find the values of a and b as well as zeroes of the given polynomial.
If x + 2a is a factor of a5 -4a2x3 +2x + 2a +3, then find the value of a.
The value of `k`, if `x^2+2x+k` is a factor of `2x^4+x^3-14x^2+5x+6` is
If `(x+a)`is a factor of `2x^2+2a x+5x+10`, find `a`.
Factorise the following : `(i) 4x^(2)+20x+25 " " (ii) 9y^(2)-66yz+121z^(2) " " (iii) (2x+(1)/(3))^(2)-(x-(1)/(2))^(2)`
Factorise:9y2 – 66yz + 121z2