Question

Exmine whether x+2 is a factor of x^3+2x^2+3x+6

Answer 1

Answer: Yes it is a factor

Step-by-step explanation:

By factor theorem,if the value of polynomial p(x) is zero at x=c, then g(x)=x−c is a factor of p(x).

Given p(x)=x  

3

+2x  

2

+3x+6 and g(x)=x+2

To find value of c,  

g(x)=0 then c=−2  

if we replace x by −2 we get,

p(−2)=(−2)  

3

+2(−2)  

2

+3(−2)+6

p(−2)=−8+8−6+6

p(−2)=0

Therefore, x+2 is factor of x  

3

+2x  

2

+3x+6