Question

50. Use the factor theorem to determine whether g (x) is a factor of p (x)
in the following case:
p(x) = 22-23 1, g(x)=x+1​

Answer 1

Answer:

(i) Apply factor theorem 

x+1=0

So x=−1

2x3+x2−2x−1

Replace x by −1, we get

2(−1)3+(−1)2−2(−1)−1=−2+1+2−1=0

Reminder is 0 so that x+1 is a factor of 2x3+x2−2x−1  

(ii) Apply factor theorem 

x+2=0 

So x=−2 

x3+3x2+3x+1

Replace x by −2, we get

(−2)3+3(−2)2+3(−2)+1=−8+12−6+1=1

Reminder is 1 so that x+2 is not a factor of x3+3x2+3x+1

(iii) Apply factor theorem 

x−3=0 

So x=3 

x3−4x2+x+6

Replace x by 3, we get

(3)