Simple factoring: Trying to factor 3x^2-2x-8... been so long, p/s gives -24 means -12 and +2..then what?

Question

Ok while I thank you guys for your quick response w/ answers, I was more curious to the process then the final answer. I guess product sum would give me -6 and +4... how do i plug those in to the original equation? The only thing I can think to do is (3x^2-6x)(-2x+4) but I don't think thats right..

Answer 1

(3x+4)(x-2)
3x+4=0
3x=-4
x=-4/3

x-2=0
x=2

Answer 2

OK
The quadratic equation represents a curve ,, or cylinder, or some geometric shape.

This means that,
f(x)= -(3x^2-2x-8)

For every value of x that you enter into the equation, you will get a value for f(x)
If you let f(x) = the Y coordinate on a graph
and x = the X coordinate, you will be able to graph the quadratic equation.

Let x=0 ,,,, (3x^2 -2x -8)
3 times 0^2 = 0
-2 times 0 = 0
-8

hence when x=0 then f(x)= -8

the first coordinate is _ (0,-8)

Let x=1 , then f(x) = -7 (1, -7)

let x= -1 the n f(x) = -3 (-1, -3)

let x =2 then f(x) = 2 (2,2)

let x= -2 then f(x) = 8 (-2,8)

What it is is a parabola with its apex at (0.-8)
opening upward, and continuing to expand infinatelyt

if you solved the equation for (3x^2-2x-8)=0
that gives you is the value of x as it crosses 0- on the y axis.

Solving for y=0 is only one point of the curve,, actually it is two points because as you now see by your graph , x can have two values, that will give y=0. one number is 2 the other is probably an irreational number like the square root of 3

With a quadratic you either factor it or graph it
in factoring you ar NOT setting (3x^2 -2x -8) =0
you are looking for the multiples of 2 two simpler
equation sthat will yield (3X2-2x-8 when multiplied together

if you multiply *
(3x+4) times (x -2) = (3x^2 -2x -8)
(x times 3x = 3x^2
x times 4 = 4x
-2 times 3x = -6x
-2 times +4 = 9

factoring is the reverse of multiplying
it is quadratic dividion
you start by testing out ( x-2) times (3x +4)
because the 2 and 4 will give a minus 8,

and keep using and trial and error until it becomes clear..

Answer 3

3 |1 3
-2|
-8|-2 4
As you can see, 1 and 3 are divisors of 3.
and -2 and 4 are divisors of -8.
Now, (-2 * 3) + (1*4)= -2 which is the coefficient of x.
So, you can factor the expression as follows.
(x-2)*(3x+4)=0

Answer 4

3x^2-2x-8
(3x+4)(x-2)

3x+4=0
3x= -4
x= -4/3

x-2=0
x=2

Answer 5

3x² - 2x - 8 = 0

3x² - 6x + 4x - 8

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

(3x + 4)(x - 2)

- - - - - - - - - -s-

Answer 6

(3x+4)(x-2)