Question

use the factor theorem to determine whether g(x) is a factor of p(x) in each of the following cases. (a). p(x)=x³-4x²+x+6, g(x)=x-3​

Answer 1

Step-by-step explanation:

Solution

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(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

3

−4x

2

+x+6