Question

Whats the factored form of 6x 2 - 8x - 8 = 0

Answer 1

`2(3x-2)(x+2)=6x^2-8x-8`

The factored form of
`6x^2-8x-8=0` is
`2(3x-2)(x+2)=0`

Explanation:

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

The way the quadratic equation was given, we can't have a factored form in the format:
`(ax-b)(cx+d)`

First, divide both sides by 2

`3x^2-4x-4=0`

Now, it is about thinking. From the equation, we will get something in the format:
`(ax-b)(cx+d)`

Let's expand this:
`(ax-b)(cx+d) = acx^2+adx-bcx-bd`

From here, we can give some values for those variables, based on the quadratic equation
`3x^2-4x-4=0`:

`(3x-b)(x+d) = 3\cdot 1\cdot x^2+3dx-b\cdot 1 \cdot x-bd= \boxed{3x^2+3dx-bx-bd}`

Once we want the middle term to be -4 and bd to be 4, we can easily evaluate the other variables.

`(3x-2)(x+2) = 3\cdot 1\cdot x^2+3(2)x-(2)\cdot 1 \cdot x-(2)(2)= \boxed{3x^2+6x-4x-4}`

Therefore,

`(3x-2)(x+2)=3x^2-4x-4`

But we are not ready yet!

This is the factored form of
`3x^2-4x-4=0`, to get the factored form of the problem equation, just multiply the factored form we got by 2.

`2(3x-2)(x+2)=6x^2-8x-8`

Answer 2

2(x -2)² = 0

Explanation:

2(x² - 4x - 4) = 0

2(x -2)² = 0

x = 2