Consider the polynomial functions defined by (x) (x 1)(x 2)(x 3), g(x) x 3 2x 2 x 2, and h(x) 3x 3 6x 2 3x 6 (a) What is the value of (1) (b) For what values, other than 1, is (x) 0 (c) Verify that g( 1) g(1) g( 2) 0 (d) Based on your answer from part (c), what do you think is the factored form of ...

f x x 1x 2x 3 gx x 3 2x 2 x 2 hx 3x 3 6x 2 3x 6 a f1 014 0 b f x is zero w ...

Consider the polynomial functions defined by (x) = (x - 1)(x - 2)(x + 3), g(x) =

Question:

Consider the polynomial functions defined by ƒ(x) = (x - 1)(x - 2)(x + 3), g(x) = x³ + 2x² - x - 2, and h(x) = 3x³ + 6x² - 3x - 6.
(a) What is the value of ƒ(1)?
(b) For what values, other than 1, is ƒ(x) = 0?
(c) Verify that g(-1) = g(1) = g(-2) = 0.
(d) Based on your answer from part (c), what do you think is the factored form of g(x)? Verify your answer by multiplying these factors and comparing with g(x).
(e) Using your answer from part (d), what is the factored form of h(x)?
(f) Based on what you have learned in this exercise, fill in the blank: If f is a polynomial and ƒ(a) = 0 for some number a, then one factor of the polynomial is ____________________.