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.  

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

then say something, tell them they won’t respect you if you don’t even have respect for your self sweetheart you need to lay it on them, all of it : )