When factored completely, the expression 3x2 - 9x + 6 is equivalent to

(1) (3x - 3) (x - 2) (3) 3 (x + 1) (x - 2)

(2) (3x + 3) (x - 2) (4) 3 (x - 1) (x - 2)

Let's see what the options look like when we multiply the expressions in brackets:

(first, i multiply both parts of the second bracked by the first part of the first bracket, and then the same with the second part of the first bracket:

(1) (3x - 3) (x - 2))

3x2 + 6x - 3x + 6 / / this is not correct

(2) (3x + 3) (x - 2)

3x2-6x+3x-6//this is not correct

(3)

3 (x + 1) (x - 2)

3 (x2-2x+x-2) / / simplifying:

3 (x2-x-2) / / multiplying:

3x2-3x-6)

- so this is not correct either

(4) 3 (x - 1) (x - 2)

3 (x2-2x - x + 2)

3 (x2-3x + 2)

3x2-9x + 6 - well, here is our winner!

3x² - 9x + 6

3 (x²) - 3 (3x) + 3 (2)

3 (x² - 3x + 2)

3 (x² - 2x - x + 2)

3 (x (x) - x (2) - 1 (x) + 1 (2))

3 (x (x - 2) - 1 (x - 2))

3 (x - 1) (x - 2)

The equation 3x² - 9x + 6 is equivalent to 3 (x - 1) (x - 2).