Question

Is (x+1)is the factor of the polynomial x 997 +x886+x775+x654+x113+1

Answer 1

Answer:

(x+1)is the factor of the polynomial x 997 +x886+x775+x654+x113+1

Step-by-step explanation:

-1+1-1+1-1+1=0

therefore (x+1)is the factor of the polynomial x 997 +x886+x775+x654+x113+1

Answer 2

(x + 1) is the factor of the polynomial $P(x):x^{997}+x^{886}+x^{775}+x^{654}+x^{113}+1$, proved.

Step-by-step explanation:

Given,

(x + 1) is the factor of the polynomial $P(x):x^{997}+x^{886}+x^{775}+x^{654}+x^{113}+1$

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

∵ x + 1 = 0

⇒ x = - 1

Put x = - 1 in P(x), we get

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

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

= 3 - 3

= 0, proved.

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