Question

Check whether (X+1) is a factor of the polynomial. X power 4+x power 3+X power 2-5x+1. Justify you answer .

Answer 1

No , (x+1) is not a factor of $x^{4} + x^{3} +x^{2} -5x+1$

x+1 =0

x = -1

if i put the value of x as -1 we will not get 0 hence its not a factor

=  $x^{4} + x^{3} +x^{2} -5x+1$

= $(-1)^{4} + (-1)^{3} +(-1)^{2} -5(1-1)+1$

= 1 - 1 + 1 + 5 + 1

=6 ≠ 0