SOLUTION: can you please factor this problem for me and show how it is done: x squared + 6x - 72

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Question 137873: can you please factor this problem for me and show how it is done:
x squared + 6x - 72
Found 3 solutions by ankor@dixie-net.com, Fombitz, Edwin McCravy:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
can you please factor this problem for me and show how it is done:
x^2 + 6x - 72 = 0
:
Look at the 3rd term, it's negative so on one factor will be positive and one negative.
:
find two factors of 72 that differ by 6 (coefficient of x), the larger one will be positive because 6 is positive
:
(x + 12)(x - 6)
:
FOIL to check it

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B6x-72=%28x%2Ba%29%28x%2Bb%29
a and b are constants that solve these equations.
ab=-72
a%2Bb=6
First, look at factors of 72.
1,72
2,36
3,24
4,18
6,12
8,9
Then look for combinations of the factors where the sum or difference might be 6.
6 and 12 look like a good bet.
Now we can match the sign (positive or negative) of each factor to solve the two equations.
Since the product is -72, one of the factors is negative.
Since the sum is positive, the smaller number (6) must be negative.
a=12 and b=-6 meets all of our criteria.
x%5E2%2B6x-72=%28x%2Ba%29%28x%2Bb%29
x%5E2%2B6x-72=%28x%2B12%29%28x-6%29

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
can you please factor this problem for me and show how it is done:
x² + 6x - 72

Write this:

(x    )(x     )

Look at the 72 of " x² + 6x - 72 "

It is negative, so think "SUBTRACT". 
(If it had been positive you would think "ADD")

Look at the 6 of " x² + 6x - 72 ".

Think of two whole numbers that when multiplied 
give 72 and, when SUBTRACTED, give 6?

Go thru pairs of integers which multiply to give 
72, and see if when you SUBTRACT them, larger
minus smaller, you get 6.

72 = 1x72, but 72-1 = 70, not 6
72 = 2x36, but 36-2 = 34, not 6
72 = 3x24, but 24-3 = 21, not 6
72 = 4x18, but 18-4 = 14, not 6
72 = 6x12, and 12-6 = 6.  Hey that's it!

Now write just the 6 and the 12 at the 
right ends of those two parentheses:

So you have this now:

(x   6)(x   12) 

Now look at the sign before the middle 
term of " x² + 6x - 72 ". It is plus, 
so put a plus next to the larger number, 
which is 12.  So now you have

(x   6)(x + 12)

Now you only need to find what sign to 
put in the first parentheses.

Since the last term of " x² + 6x - 72 " 
is negative, put the OPPOSITE sign before 
the 6 that you put before the 12.  Since
you oput a plus sign before the 12, you 
will put a minus sign before the 6. 

(x - 6)(x + 12)

(If it were positive, you would have put 
the SAME sign instead.)

Edwin