Question

Is (x+1) is a factor of polynomial x⁹⁹⁷+ x⁸⁸⁶+x⁷⁷⁵+x⁶⁵⁴+1 ?

with full solution step by step​

Answer 1

Answer:

No x + 1 is not a factor

Step to step explanation:

if ( x + 1 ) is a factor, then x = -1

now substitute:

For odd powers the value will be -1 and for even powers it will be 1 itself, for example - $1^{2}$ = -1 x -1 = 1 , whereas - $1^{3}$ = -1 x -1 x -1 = -1

so $x^{997} = -1, x^{886} = 1, x^{775} = -1, x^{654} = 1$

Now substituting the values:

-1 + 1 - 1 + 1 + 1 = -2 +3

                       = 1

If ( x + 1 ) was a factor, then the remainder should have been 0

but since the remainder is 1, ( x + 1 ) is not a factor.