Question

check the accuracy of the given statement :(x+2) is factor of p(x)= x^(3)+x^(2)+x+2​

Answer 1

Answer:

To Prove (x+2) is a factor of p(x)=x3+x2+x+2

Prove (x+2) is a factor of p(x)=x3+x2+x+2⇒x+2=0

Prove (x+2) is a factor of p(x)=x3+x2+x+2⇒x+2=0⇒x=−2

Prove (x+2) is a factor of p(x)=x3+x2+x+2⇒x+2=0⇒x=−2Putting value of x=−2 in p(x)

Prove (x+2) is a factor of p(x)=x3+x2+x+2⇒x+2=0⇒x=−2Putting value of x=−2 in p(x)=x3+x2+x+2

Prove (x+2) is a factor of p(x)=x3+x2+x+2⇒x+2=0⇒x=−2Putting value of x=−2 in p(x)=x3+x2+x+2=(−2)3+(−2)2+(−2)+2

Prove (x+2) is a factor of p(x)=x3+x2+x+2⇒x+2=0⇒x=−2Putting value of x=−2 in p(x)=x3+x2+x+2=(−2)3+(−2)2+(−2)+2=−8+4−2+2

Prove (x+2) is a factor of p(x)=x3+x2+x+2⇒x+2=0⇒x=−2Putting value of x=−2 in p(x)=x3+x2+x+2=(−2)3+(−2)2+(−2)+2=−8+4−2+2=−4.

Prove (x+2) is a factor of p(x)=x3+x2+x+2⇒x+2=0⇒x=−2Putting value of x=−2 in p(x)=x3+x2+x+2=(−2)3+(−2)2+(−2)+2=−8+4−2+2=−4.so, it is not equal  to zero so x+2 is not a factor.

Prove (x+2) is a factor of p(x)=x3+x2+x+2⇒x+2=0⇒x=−2Putting value of x=−2 in p(x)=x3+x2+x+2=(−2)3+(−2)2+(−2)+2=−8+4−2+2=−4.so, it is not equal  to zero so x+2 is not a factor.Hence, solve.

Answer 2

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