Math factoring help!!! 6x^2+10x-4?

Question

Please help! How do I do this! Thanks so much in advance.

Answer 1

multiply the beginning and the end digit together (-24) and find another multiplication pair that adds up to the middle number which is 10.

those numbers will be 12 and -2 since 12-2=10 and 12(-2)=-24. (remember that the multiplication pairs won't always be the ones you started out with, the ones you multiplied in the first step)

plug those digits in replace of the 10x. separate them with parentheses so that they are added to beginning and to the end of the equation. (6x^2+12x)+(-2x+4). since it's best to have the plus sign in between the parentheses, these numbers should be reverse to (6x^2-2x)+(12x+4).

Now find the greatest common factor (GCF) in both. the first set is 2, the second is 4.

divide that from the equations like reverse distributive property. it would look like this 2x(3x-1)+4(3x+1). when doing actual distibutive property, the equation should look exactly like (6x^2+2x)+(12x+4)

the equation in the parentheses should be the same which is why it is important to keep the X in the first set so that there can be a square. since there isnt a square in the second parentheses, the stays within the parentheses.

the numbers outside the parentheses will be added and the numbers inside the parentheses will remain: (2x+4)(3x-1)
notice the standard form in both ^^

sry its too long. but i hope im informative!!

Answer 2

multiply the number (coefficient) with x2 by the number without the x, (constant) so in this one, 6*-4 = -24

you want to find two numbers so that they Multiply together to get -24, but Add together to make +10

(1,-24 ) or ( 2, -12 ) or ( 4, -6) or (-1,24 ) or ( -2,12) or (-4,6)

1 - 24 = -23 ... nope
2 - 12 = -10 ... nope
4 - 6 = -2 ... nope
-1 + 24 = 23 ... nope
-2 + 12 = 10 ... YES! we can stop and move on...

now, rewrite the equation with the +10x rewritten into two terms, using the two numbers we just found, -2 and +12:

6x² + 12x -2x -4

then group the first two, and the last two, and factor whatever you can from each one:

(6x² + 12x) + (-2x - 4)
6x(x + 2) + -2(x + 2)

we got the x+2 out of both, so we can change this to:

(x + 2)(6x -2)

Be Careful of the Signs as you go through each step!

Answer 3

(2x + 4 )(3x -1)
I got my answer by guessing and checking.

Foil
2x(3x) + 2x(-1) + 4(3x) + 4(-1)= 6x^2 + 10x - 4
First......outside..inside....last

Some common sense is involved. The first numbers multiplied together have to give you 6x^2 and the last two--negative 4. You just have to figure out which numbers fit.

Answer 4

6x^2 + 10x - 4

2(3x^2 + 5x - 2) {common factor}

2(3x^2 + 6x - x - 2)

2[3x(x + 2) - 1(x + 2)] {rewrite for grouping}

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

Answer 5

The first answer is correct.

(3x-1)(2x+4)

3x and 2x give the product 6x^2

the sum of the cross products -2x and 12 x yields 10x

the product of -1 and 4 yields - 4

Voila! QED

Answer 6

(3x - 1)(2x + 4)
Check
6x² + 12x - 2x - 4
6x² + 10x - 4

Answer 7

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

Answer 8

(3x-1)(2x+4)