Factor by grouping (sometimes called the ac-method).
8x^2+2x-3
first, choose a form with appropriate signs.
then, fill in the blanks with numbers to be used for grouping.
finally, show the factorization.

Step-by-step explanation:

The arc method is basically finding what the a and c coefficients multiply to, and then finding the factors of that that add up to b.

Since we have the quadratic in the ax^2+bx+c form we don't have to adjust anything.  Now, a = 8, b = 2 and c = -3.  a*c = -24 so now we want to find all the factors of that.

-1 and 24

1 and -24

-2 and 12

2 and -12

-3 and 8

3 and -8

-4 and 6

4 and -6

And after that they repeat.  It is important to note that you can use negative on either side, or if a*c was a positive number you could multiply two negatives like 24 can be  and 12 as well as -1 and -12.

Now we want to look at all the factor pairs  and find one that add together to equal 2 because b = 2.  -4 + 6 does it, so there's our choice.  Now we can rewrite the original quadratic as 8x^2-4x+6x-3.  You can check that this is equivalent by combining like terms It's the same as rewriting it as 8x^2+2x-2-1 because -2 and -1 will combine to get -3.  Anyway, now we can factor.

8x^2-4x+6x-3  You can imagine there being two sets of parenthesis.

( 8x^2-4x)+(+6x-3)  Now from here we can factor something out of each parenthesis.  e can factor out 4x fromt he first and 3 from the second.

4x(2x-1)+3(2x-3)  Now, it may not be obvious but you can factor 2x-3 from each term.  If that's not clear pretend 2x-3 = u

4xu + 3u  Now hopefully it is clear you can factor out this u

u(4x+3)  Then we know u = 2x-3 so

(2x-3)(4x+3)  And it's factored.

I do want to mention you could have done this with  8x^2+6x-4x-3 with the +6 and -4 switched.  I won't go through it here but it may help to do it yourself if you still don't quite understand.  Let me know if there is something I can further explain though.  

24

step-by-step explanation:

if it takes 8 pounds to make 12 divide 12 by 8 and you get 1.5, 1.5 x 16 = 24