Question

Check wether (x+1) is a factor of the polynomial.x^4+x^3+x^2-5x+1.Justify your answer.

Answer 1

hey frnd....
=> (x+1) = 0
=> x=-1
now we have to put this value of x in the given polynomial and Check whether it's a factor or not.
${x}^{4} + {x}^{3} + {x}^{2} - 5x + 1 \\ {( - 1)}^{4} + { ( - 1)}^{3} + {( - 1)}^{2} - 5( - 1) + 1 \\ 1 - 1 + 1 + 5 + 1 \\ 7$
now 7 comes in remainder..... hence -1 is not zero of the given polynomial
so..... (x+1) is not factor of given polynomial.

HOPE THIS HELP YOU ☺☺