-2x^2 -4x + 6 - factorize?

-2x² - 4x + 6
= -2 (x² + 2x - 3) <--- 1st, take out the common factor, that is -2
= -2 (x+3) (x-1) <--- 2nd, use cross method to find out the final answer

I hope I can help you =]

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

In both cases, the first thing to do is get rid of the obvious constant common factors. In (a) that's a 2; in (b) I factored out a -2 because it's a whole lot easier to get your head around the rest if it's in the usual form, and reversing the signs is the easiest way. a) 12x^2 - 14x - 6 = 2 * (6x^2 - 7x - 3) = 2 * (3x + 1) * (2x - 3) b) 12 - 2x - 4x^2 = (-2) * (2x^2 + x - 6) = ( -2) * (x + 2) * (2x - 3) [or if your instructor wants that minus sign left embedded in one of the expressions,] = 2 * (x + 2) * (3 - 2x) I'm afraid that I am several decades rusty on this stuff, and my factoring technique (once I get it down to an easy expression) consists of looking for a combination of pluses and minuses that will add up right. For example, in the first one I needed to get factors of 6 and factors of -3 that would, when multiplied in the correct combinations, add up to -7, so I realized that (-3)*3 and 1*2 were the ones that would do it. But aside from using the quadratic formula (a tactic only desirable when desperate, as far as I'm concerned), it's just a matter of juggling the numbers in my head. Sorry if I can't be more explicit. The second case is similar; I've got factors of 2 and factors of -6 and I need a 1, so 2*2 and 1*(-3) worked.

(-2) (x² + 2 - 3)
(-2) (x + 3)(x - 1)

-2x^2 - 4x + 6
= -2(x^2 + 2x - 3)
= -2(x^2 + 3x - x - 3)
= -2[(x^2 + 3x) - (x + 3)]
= -2[x(x + 3) - 1(x + 3)]
= -2(x + 3)(x - 1)

Factorize:

-2x^2 - 4x + 6

Reorder the terms:

6 - 4x - 2x^2

Factor out the Greatest Common Factor (GCF) = 2

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

Factor a trinomial

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

Multiply using the FOIL Method to confirm (check and test) the answer.

1 x 3 = 3

1 x x = 1x

-1x x 3 = -3x

-1x x x = -1x^2

3 + 1x - 3x - 1x^2

3 - 2x - 1x^2

2(3 - 2x - 1x^2)

The answer is:

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

The first answer (shhrewd's answer) is wrong!!
This is how you do it
what numbers multiply to give you six (the last number without an x) 3 and 2, 6 and 1, -3 and -2, -6 and -1 because we have the -2x^2 we have to work out which number we can put in the brackets (-2x )(x ) that will multiply out to give us the function. It's trial and error at this point. I got 3 and 2.
therefore the answer is (-2x+2)(x+3). Be careful, the order in which you put the numbers in the brackets will change the answer e.g. (-2x +3)(x+2) and (-2x +2)(x+3) are not the same. Final answer is (-2x+2)(x+3).
Proof
To prove it multiply out of the brackets and see if it gives you the same function...if not it's wrong.
(-2x + 2)(x+3) = -2x^2 -6x +2x+ 6 { -6x + 2x = -4x so you get }
= -2x^2 - 4x +6
hope I helped

the first answer given is -2x(x+3)(x-1) multiply this out of the brackets and you get
(-2x-3)(x-1)
= -2x^2 +2x - 3x +3
=-2x^2 -x + 3 which is not the function you want

take a 2 out of all of it = 2(-x^2 -2x + 3)

now split -x^2 into two factors 2(-x )(x )

now you need two factors that multiply to 3 and add to but adds to -2 which are -2 and -1 which then simplifies into 2(-x - 1)(x - 2)

But you are not done yet, notice in the in the first parenthesis you can take out a -1

so it is now 2 times -1( x +1)(x - 2) which =


-2( x +1)(x - 2) that is your answer !