Question

use the factor theorem to determine whether g(x) is a factor of p(x) in each of the following cases
p(x) =2x³+x²-2x-1, g(x) =x+1​

Answer 1

Answer:

Step-by-step explanation:

(i) Apply factor theorem  

x+1=0

So x=−1

2x  

3

+x  

2

−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 2x  

3

+x  

2

−2x−1  

(ii) Apply factor theorem  

x+2=0  

So x=−2  

x  

3

+3x  

2

+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 x  

3

+3x  

2

+3x+1

(iii) Apply factor theorem  

x−3=0  

So x=3  

x  

3

−4x  

2

+x+6

Replace x by 3, we get

(3)  

3

−4(3)  

2

+(3)−1=27−36+3+6=0

Reminder is 0 so that x−3 is a factor of x  

Answer 2

Answer:

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