Question

Q5. Show that p-1 is a factor of
${p}^{10}$
-1 and also
${p}^{11}$
-1.​

Answer 1

Answer:

if p-1 is a factor of a polynomial P(p) then at p= 1 ,the polynomial becomes zero,ie. P(1)=0

let's check, whether p-1 is a factor of

p^10 -1or not.

putting,p=1 in the polynomial,

we get,

=> (1)^10 -1

=> 1-1

=> 0

since,the value of polynomial at p=1 is zero,thus p-1 is factor of the polynomial

p^10-1.

now let's check whether p-1 is a factor of p^11-1 or not.

putting,p=1 in the polynomial,

we get,

=> (1)^11-1

=> 1-1

=> 0

since the value of polynomial at p=1 is zero,thus p-1 is the factor of polynomial

p^11-1.

{ note that p-1 is a factor of polynomial

p^n-1,for every natural value of n}

thank you,

I hope it would help you

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