Question

Factored form of the given equation
6x2+2x-8=

Answer 1

(
`x-1`) and (
`x+(4)/(3))` are the factors of the given equation

It can be written as
`6x^2+2x-8=(x-1)(x+(4)/(3))`

Explanation:

Given quadratic equation is
`6x^2+2x-8=0`

To find the factored form of the given equation :

`6x^2+2x-8=0`

By using the formula for quadratic equation
`ax^2+bx+c=0` then the solution is
`x=(-b\pm √(b^2-4ac))/(2a)` where a and b are coefficients of
`x^2` and x respectively

`x=(-b\pm √(b^2-4ac))/(2a)`

Substitute a=6, b=2 and c=-8 in the above equation we get

`x=(-2\pm √(2^2-4(6)(-8)))/(2(6))`

`=(-2\pm √(4+192))/(12)`

`=(-2\pm √(196))/(12)`

`=(-2\pm 14)/(12)`

`x=(-2\pm 14)/(12)`

Therefore
`x=(-2+14)/(12)` and
`x=(-2-14)/(12)`

`x=(12)/(12)` and
`x=(-16)/(12)`

`x=1` and
`x=(-4)/(3)`

Therefore (
`x-1`) and
`(x+(4)/(3))` are the factors of the given equation

It can be written as
`6x^2+2x-8=(x-1)(x+(4)/(3))`