Question

HELP ASAP!!!!!!!!!!!!!

Use the remainder theorem to completely factor p(x) = x^3 - 6x^2 + 11x - 6. SHOW YOUR WORK.

Answer 1

p(x) = (x - 1)(x - 2(x - 3)

note that p(1) = 1 - 6 + 11 - 6 = 0

x = 1 is a root ⇒ (x - 1 ) is a factor

1 | 1 - 6 + 11 - 6

↓ 1 - 5 +6

1 - 5 6 0

p(x) = (x - 1)(x² - 5x + 6 ) = (x - 1)(x - 2)(x - 3)