Question

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2x 3 + x 2 − 2x − 1, g(x) = x + 1 (ii) p(x) = x 3 + 3x 2 + 3x + 1, g(x) = x + 2 (iii) p(x) = x 3 − 4 x 2 + x + 6, g(x) = x − 3

Answer 1

Answer:

your answer is here ....

Answer 2

Answer:

factor

not factor

factor

Step-by-step explanation:

p(x) = 2x³ + x² - 2x - 1

g(x) = x + 1 is factor if  for x = -1  the p(x) =0

=> p(-1) = 0

p(-1) = 2(-1)³ +(-1)² -2(-1) - 1  = -2 + 1 + 2 - 1 = 0

Hence g(x) is factor of p(x)

p(x) = x³ + 3x² + 3x + 1

g(x) = x + 2 is factor if  for x = -2  the p(x) =0

=> p(-2) = 0

p(-2) = (-2)³ +3(-2)² +3(-2) + 1  = -8 + 12 - 6 + 1 = -1 ≠ 0

Hence g(x) is not a factor of p(x)

p(x) = x³ - 4x² + x + 6

g(x) = x -3 is factor if  for x = 3  the p(x) =0

=> p(3) = 0

p(3) = 3³ -4(3)² +3 + 6  = 27 - 36 + 3 + 6 = 0

Hence g(x) is factor of p(x)