Im still so confused with factoring?

Question

I think I understadn factor one minute and then not the next. He is how someone showed me how to factor x^2+5x+6=0
I factor out x^2 and get (x+a)(x+b) and then do a+b=5 and a*b=6 so u end up with 2 and 3.

However then I look at another example and its answer and im confused again 3x^2-18x-48=0 so I split them up again and divide by three and get 3(x^2-6x-16)=0 so why is it (x-8)(x+2) 8*2=16 but 8+2 isnt 6. HELP PLEASE!!!

Answer 1

With your method, you need to include the signs of each part, as in (x-8) = (x + (-8)), so a = -8, not 8. From there, -8 + 2 = -6, and -8 * 2 = -16. Then it works!
Hope this helps!

Answer 2

The problem is not serious there is a slight gap in your understanding.
when you take
x^2+mx +c ( i use m insted of b as you have used b in factoring)
you should find 2 factors of c so that sum is m

factor x^2+5x+6=0
I factor out x^2 and get (x+a)(x+b) and then do a+b=5 and a*b=6 so u end up with 2 and 3.
The above approach was right as c = 6 and you used correctly

in the second problem (x^2-6x-16)=0 so why is it (x-8)(x+2) 8*2=16 but 8+2 isnt 6. HELP PLEASE!!!

you should see that c = - 16 and not 16 and m = -6 and not 6. you took only the posiv\tive value

factor -16 so that sum is -6 it is -8 and 2.

sum = -8+(2) = -6
tou took only positive value and ran into problem
in your steps
a+b = -6
and ab = -16

I hope i clarified

Answer 3

x^2+5x+6=0

x^2 is also 1x^2 (the 1 is understood to be before the x.)
You can break down 1 only with (1x1), no other whole numbers will multiply to give you that answer.

x^2+5x+6=0


6 is broken down into
(1x6) or (2x3)

Now, you need to try to get a combination of the “factors” to give you the number in the middle (5x in this case.)


(1x1) and (2x3) are the best bet in this case. Since your 6 is positive (the number without any x’s), you will use the same sign in both sets below, regardless of which sets of numbers you use. If it were negative, you would use different signs.


(1x + 2) (1x X 3)

To check if they are the correct ones, you are going to do some quick math. Multiply the inner and outer numbers separately and get an answer based on the two of them.
(sorry, formatting is making this difficult to show)
(1x + 2) (1x X 3)
.1x........X.........3 = 3x (1x X 3 = 3x)

(1x + 2) (1x X 3)
..........2 X1x........= 2x (2 X 1x = 2x)

2x + 3x = 5x - the middle number of your equation.



Put each set of numbers from your parenthesizes equal to 0

1x + 2 = 0

1x + 3 = 0

Finish the equations by solving for x

1x = -2

1x = -3

If you put either number back in the original equation, it will work:

(-2)^2 + 5(-2) +6 (-3)^2 + 5(-3) +6 =0
4 + (-10) +6 = 0 9 + (-15) + 6 = 0
4 - 10 + 6 = 0 9 - 16 + 6 = 0


This would not work if you had used the 1 and 6 instead.

(1x + 1) (1x + 6)

1x X 6 = 6x

1 X 1x = 1x

6x + 1x = 7x


I hope I did not just confuse you with all of that. In a nut shell, you are looking to multiply the “factors” of the first and last numbers to get the exact number in the middle. If you can do this, the equations you use will show you what x can be.

Answer 4

-8 + 2 = -6

Answer 5

I can't help in the process because I've always just been able to factor things, I don't really have a process, I just do it by trial and error. The answer, on the other hand, is (3x+6)(x-8).