Factor Theorem for Polynomials

Question

Use the Factor Theorem to show that x−c is a factor of P(x) for the given values of c, where

P(x)= x^3−4x^2+9x−6, c=1

1) The quotient is ?

2) The remainder is ?

Answer 1

1) p(1) = 1 - 4 + 9 - 6 = 0. So, by factor theorem (x - 1) is a factor of p(x0 = x³ - x² - 3x² + 3x + 6x - 6 =

(x - 1)(x² - 3x + 6) and quotient q(x) = x² - 3x + 6

2 The remainder r = 0