Question

is(X+1) is factor of the polynomial x⁹⁹⁷+x⁸⁸⁶+x⁷⁷⁵+x⁶⁵⁴+x¹¹³+1?​

Answer 1

Answer:

X = -1

Step-by-step explanation:

${ - 1}^{997} + { - 1}^{886} + { - 1}^{775} + { - 1}^{654} + { - 1}^{113} + 1 \\ = - 1 + 1 - 1 + 1 - 1 + 1 = 0$

Answer 2

Answer:

( x + 1 ) is the factor of the polynomial p (x) : x⁹⁹⁷ + x⁸⁸⁶ + x⁷⁷⁵ + x⁶⁵⁴ + 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 d factor of the polynomial p ( x ) : x⁹⁹⁷ + x⁸⁸⁶ + x⁷⁷⁵ + x⁶⁵⁴ + x¹¹³ + 1 , proved.

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