Question

How do you factor the trinomial `24x^2 - 11x - 3 =3x`?

Answer 1

`24x^2-11x-3=3xcolor(white)("XXX")rArrcolor(white)("XXX")color(green)((6x+1)(4x-3)=0)`

Explanation:

Rewrite the given equation in standard form as:
`color(white)("XXX")24x^2-14x-3=0`

Use the AC method with `A=24` and `C=(-3)`
(see: http://www.bates.ctc.edu/Documents/Tutoring%20Center/Tutoring_ACmethodwksheet.pdf)

We are looking for factors of `24xx(-3)` whose sum is `(-14)`

Since `B=(-14)<0` we can reduce the number of factor we examine by only looking at those factor pairs with the larger magnitude factor negative.

`{: (,,color(white)("XXX"),"Difference"), (,-24xx3,color(white)("XXX"),-21), ((-24/2)xx(3xx2)=, -12xx6,color(white)("XXX"),-6), ((-24/3)xx(3xx3)=,8xx-9,color(white)("XXX"),-1), ((-24/4)xx(3xx4)=,6xx-12,color(white)("XXX"),-6), ((-24/6)xx(3xx6)=,4xx-18,color(white)("XXX"),-14) :}`

Having found the necessary factors we can stop looking and re-write our equation as:
`color(white)("XXX")24x^2-18x+4x-3=0`

`color(white)("XXX")6x(4x-3)+1(4x-3) =0`

`color(white)("XXX")(6x+1)(4x-3)=0`