What is the completely factored form of f(x) = x³ - 2x² - 5x + 6?

Solution:

Given, f(x) = x³ - 2x² - 5x + 6

We have to find the complete factored form of f(x).

Consider (x - 1) as a factor of f(x).

Let us check (x - 1) is a factor of f(x).

f(1) = (1)³ - 2(1)² - 5(1) + 6

= 1 - 2 - 5 + 6

= 6 - 6

= 0

f(1) = 0

Therefore, (x - 1) is a factor of f(x) = x³ - 2x² - 5x + 6.

By long division,

Now, find the factor of x² - x - 6

x² - x - 6 = 0

x² - 3x + 2x - 6 = 0

x(x - 3) + 2(x - 3) = 0

(x + 2)(x - 3) = 0

Therefore, the factored form is (x - 1)(x + 2) and (x - 3).

What is the completely factored form of f(x) = x³ - 2x² - 5x + 6?

Summary:

The completely factored form of f(x) = x³ - 2x² - 5x + 6 is (x - 1)(x + 2) and (x - 3).