Question

use the factor theorem to determine whether g(x) is a factor of p(x), where p(x) = x³+2x²-5x-6 and g(x) = x-2

Answer 1

Answer:

i) Apply factor theorem

x+1=0

So x=−1

refer the attachment this is the correct answer

Answer 2

Answer:

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

Sox = -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)³-4(3)² + (3) -1 = 27-36+3+

6=0

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

x³-4x²+x+6