Question

How do you factor the trinomial `6x² - x - 2`?

Answer 1

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

Explanation:

Factors of 6 are:`" "1xx6 " and "2xx3`
Factors of 2 are:`" " 1xx2`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given:`" "6x^2-x-2`

Notice that we have `-2` in the given expression
This means that we must have the format of

`(?xcolor(red)(-1))(?xcolor(red)(+2))" or "(?xcolor(red)(-2))(?xcolor(red)(+1))"`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Attempt 1")`

`(2x-1)(3x+2) = 6x^2-3x+4x-2 = 6x^2color(red)(+x)-2" "color(red)("Fail")`

`color(blue)("Attempt 2")`

`(2x+1)(3x-2) ->6x^2 +3x-4x-2`

`= 6x^2color(green)(-x)-2" "color(green)("Works!")`

Answer 2

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

Explanation:

The standard form of a trinomial is `ax^2 + bx + c`

To factor consider factors of product ac that sum to b , the coefficient of the x term.

For `6x^2 - x - 2`

a = 6 , b = -1 and c = -2

consider factors of ac =`( 6xx-2 )= -12`

factors of -12 are ± (1,2,3,4,6,12 ). - 4 and 3 are the required factors
as - 4 + 3 = - 1 = b.

Now replace - x by 3x - 4x

hence: `6x^2 + 3x - 4x - 2 = 3x(2x+1) - 2 (2x + 1 )`

there is now a common factor of (2x + 1 )

`rArr 6x^2 - x - 2 = (2x + 1 )(3x - 2 )`