SOLUTION: This particular problem that I'm working on says Divide x square+10x+24 over x+4. For a problem like this, is the Distributive Property recommended?

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Question 116567: This particular problem that I'm working on says Divide x square+10x+24 over x+4. For a problem like this, is the Distributive Property recommended?
Found 3 solutions by MathLover1, bucky, Edwin McCravy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The Distributive Property is handy to help you get rid of parentheses.
a%28b+%2B+c%29+=+ab+%2B+ac+

%28x+%5E2%2B10x%2B24%29%2F+%28x%2B4%29………. replace 10x with 4x+%2B+6x
%28x+%5E2+%2B+4x+%2B+6x+%2B+24%29%2F+%28x%2B4%29………. group the first two terms together and the last two terms together like this:

%28%28x+%5E2+%2B+4x%29+%2B+%286x+%2B+24%29%29%2F+%28x%2B4%29………. factor a x out of the first group and factor a 6 out of the second group
%28x%28x+%2B+4%29+%2B+6%28x+%2B+4%29%29%2F+%28x%2B4%29………. we have a common term x%2B4 and we can combine the two terms
%28x+%2B+6%29%28x+%2B+4%29%2F+%28x%2B4%29……….cancel x%2B4

x+%2B+6……….your answer

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
This is a typical "set-up" math problem meant to teach you something.
.
You might guess that the quadratic expression x%5E2+%2B+10x+%2B+24 can be factored. And
since the divisor is x+%2B+4 you might also guess that in this "set-up" it will be one
of the factors of the quadratic.
.
As a matter of fact, that's just exactly what happens. Start with:
.
%28x%5E2+%2B+10x+%2B+24%29%2F%28x+%2B+4%29
.
Factor the quadratic numerator to get:
.
%28%28x+%2B+6%29%28x%2B4%29%29%2F%28x+%2B+4%29
.
Cancel the like terms in the numerator and denominator:
.
%28%28x+%2B+6%29cross%28x%2B4%29%29%2Fcross%28x+%2B+4%29
.
And you are left with the answer:
.
x+%2B+6
.
Don't always expect things to work out this nicely. Lots of times in "real life" the quadratic
can not be factored ... or the denominator is not one of the factors of the quadratic ...
or some other "glitch". This problem just happens to be an example of a process that you might
try as a method of solving the problem.
.
Hope this helps you to learn a little more about this method of problem solving.
.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
This particular problem that I'm working on says Divide: %28x%5E2%2B10x%2B24%29%2F%28x%2B4%29. For a problem like this, is the Distributive Property recommended? 

No, the distributive property is recommended only when the denominator
contains ONLY ONE TERM.  But the denominator here is x+4 which contains
TWO terms.

If you were to use the distributive property you would have:

%28x%5E2%2B10x%2B24%29%2F%28x%2B4%29

x%5E2%2F%28x%2B4%29%2B%2810x%29%2F%28x%2B4%29%2B24%2F%28x%2B4%29

and none of those three fractions can be simplified.  So the
distributive law "complicates" rather than simplifies.

The correct way to simplify 

%28x%5E2%2B10x%2B24%29%2F%28x%2B4%29

is either by long division:

             x +  6
x + 4)x² + 10x + 24
      x² +  4x
            6x + 24
            6x + 24 
                  0

getting quotient x + 6,

or by factoring the numerator

%28x%5E2%2B10x%2B24%29%2F%28x%2B4%29

as

%28%28x%2B4%29%28x%2B6%29%29%2F%28x%2B4%29

and then canceling the %28x%2B4%29's,

%28cross%28x%2B4%29%28x%2B6%29%29%2Fcross%28x+%2B+4%29

 leaving

x%2B6

Edwin