Question

10. Is (x +1) is a factor of the polynomial x99+x886 + x775 + x654 +x113 + 1?​

Answer 1

Answer:

(x + 1) is the factor of the polynomial P(x):x^{997}+x^{886}+x^{775}+x^{654}+x^{113}+1P(x):x997+x886+x775+x654+x113+1 , proved.

Step-by-step explanation:

Given,

(x + 1) is the factor of the polynomial P(x):x^{997}+x^{886}+x^{775}+x^{654}+x^{113}+1P(x):x997+x886+x775+x654+x113+1

To prove that, (x + 1) is the factor of the polynomial P(x):x^{997}+x^{886}+x^{775}+x^{654}+x^{113}+1P(x):x997+x886+x775+x654+x113+1 .

∵ x + 1 = 0

⇒ x = - 1

Put x = - 1 in P(x), we get

P(-1)=(-1)^{997}+(-1)^{886}+(-1)^{775}+(-1)^{654}+(-1)^{113}+1P(−1)=(−1)997+(−1)886+(−1)775+(−1)654+(−1)113+1

= - 1 + 1 - 1 + 1 - 1 + 1

= 3 - 3

= 0, proved.

Thus, (x + 1) is the factor of the polynomial P(x):x^{997}+x^{886}+x^{775}+x^{654}+x^{113}+1P(x):x997+x886+x775+x654+x113+1 , proved.

Answer 2

Answer:

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