Is (x+1) is a factor of the polynomial x^1002 +x^923+x^856+x^177-x^29+1?
Answers
x + 1) is the factor of the polynomial P(x):x^{997}+x^{886}+x^{775}+x^{654}+x^{113}+1P(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}+1P(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}+1P(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}+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):x
997
+x
886
+x
775
+x
654
+x
113
+1 , proved.