Question

Use the factor thereom to determine whether g(x) is a factor of p(x) in the following cases : x^3-4x^2+4x+6,g(x)=x-3​

Answer 1

Answer:

pply 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  

3

−4x  

2

+x+6

Video Explanation

Solution To Question ID 463590

Answer 2

Given polynomial f(x)=x
3
−4x
2
+x+6 the factor of g(x)=x−2
If x-2 is factor then x-2=0 or x=2
Replace x in p(x) by 2 we get
f(x)=x
3
−4x
2
+x+6
f(2)=(2)
3
−4(2)
2
+(2)+6
⇒f(2)=8−16+2+6
⇒f(2)=0
So f(x) is zero by g(x) =x-2 then g(x)=(x-2) is factor of f(x)=x
3
−4x
2
−x+6