Question

x+1 is a factor of the polynomial _____ a) x3+x2 -x+1 b) x3+x2+x+1 c) x4+x3+x2x+1​

Answer 1

Answer:

b) $x^{3} +x^{2} +x+1$

Step-by-step explanation:

Factoring:  $x^{3} +x^{2} +x+1$

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  x+1  

Group 2:  $x^{3} +x^{2}$

Pull out from each group separately :

Group 1:   (x+1) • (1)

Group 2:   $(x+1).$ $(x^{2} )$

              -------------------

Add up the two groups :

              $(x+1) .$ $(x^{2} +1)$

Which is the desired factorization.

Hence we got x+1 as a factor.

Therefore x+1 is a factor of the polynomial  $x^{3} +x^{2} +x+1$