Question

x3+x2+ x+1 determine of the following polynomial​

Answer 1

Solution :

For x+a to be a factor of p(x), −a should be a zero of p(x).

(i) p(x)=x3+x2+x+1

For x+1 to be a factor of p(x), −1 should be a zero of p(x).

∴p(−1)should be 0.

p(−1)=(−1)3+(−1)2+(−1)+1=−1+1−1+1=0

⇒p(−1)=0

∴x+1 is a factor of p(x).