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.  

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~

a)(x-2)^2+(y-1)^2=9

step-by-step explanation:

(picture explains)