SOLUTION: Please show me how to divide by long division this: (3x^3+4x-1) / (x^2+1)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please show me how to divide by long division this: (3x^3+4x-1) / (x^2+1)      Log On


   

Question 242898: Please show me how to divide by long division this: (3x^3+4x-1) / (x^2+1)
Found 3 solutions by nyc_function, unlockmath, Edwin McCravy:
Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
If you give me your e-mail, I can send you the answer using paint attachment, which is far easier to read and follow. With paint, I can also draw geometric shapes.
I'll wait for your reply.
Write to: nycfunction@yahoo.com
Guido

Answer by unlockmath(1688) About Me  (Show Source):
You can put this solution on YOUR website!
Good morning,
When dividing polynomials, it is set up like simple division problems. Let's look at x^2+1 and see what we'd have to multiply to make it 3x^2 + 4x
As you can see, we'd have to multiply it by 3x. That would give us 3x^3 +3x right?
so subtract 3x^3+3x from 3x^3+4x leaves us with x. now bring down the -1 to make it x-1. Notice x^2 + 1 doesn't go into x-1 so the answer is:
3x+0 remainder x-1
(Note: I realize this might be tough to follow without showing the actual division sign)
RJ Toftness
www.math-unlock.com
you can email me directly at rjpublishers@yahoo.com if you have further questions.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%5E3%2B4x-1%29+%2F+%28x%5E2%2B1%29

You have to put in placeholder zeros for the missing powers in both the 
divisor and the dividend, and deal with 0 placeholders all through
the long division process.

You have to write 3x%5E3%2B4x-1 as 3x%5E2%2B0x%5E2%2B4x-1 and
you have to write x%5E2%2B1 as x%5E2%2B0x%2B1

Then you write this:

         
           ------------------- 
x² + 0x + 1)3x³ + 0x² + 4x - 1 

Divide %283x%5E3%29%2Fx%5E2 getting 3x and write this
above the line in line with the 4x:

                        3x
           ------------------- 
x² + 0x + 1)3x³ + 0x² + 4x - 1 

Now multiply 3x by x² + 0x + 1, getting 3x³ + 0x² + 3x,
and write it below like this, keeping like powers of x
lined up, then draw a line underneath.

                        3x
           ------------------- 
x² + 0x + 1)3x³ + 0x² + 4x - 1
            3x³ + 0x² + 3x
            --------------
                   
Now subtract (3x³ + 0x² + 4x) - (3x³ + 0x² + 3x) = 0x² + x.

(Not you must keep the placeholder zero for the x² term:


                        3x
           ------------------- 
x² + 0x + 1)3x³ + 0x² + 4x - 1
            3x³ + 0x² + 3x
            --------------
                  0x² +  x

Now bring down the next (last) term -1:

                        3x
           ------------------- 
x² + 0x + 1)3x³ + 0x² + 4x - 1
            3x³ + 0x² + 3x
            --------------
                  0x² +  x - 1

Next divide 0x%5E2%2Fx%5E2 getting 0, so write + 0
on top above the -1:

                        3x + 0
           ------------------- 
x² + 0x + 1)3x³ + 0x² + 4x - 1
            3x³ + 0x² + 3x
            --------------
                  0x² +  x - 1

Multiply 0 by x² + 0x + 1 getting 0x² + 0x + 0 and
write it at the bottom. Then draw a line:

                        3x + 0
           ------------------- 
x² + 0x + 1)3x³ + 0x² + 4x - 1
            3x³ + 0x² + 3x
            --------------
                  0x² +  x - 1
                  0x² + 0x + 0
                  ------------

Subtract: (0x² +  x - 1) - (0x² + 0x + 0) = x - 1, so

write that at the bottom:

                        3x + 0
           ------------------- 
x² + 0x + 1)3x³ + 0x² + 4x - 1
            3x³ + 0x² + 3x
            --------------
                  0x² +  x - 1
                  0x² + 0x + 0
                  ------------
                         x - 1

Now the final answer is gotten by adding the fraction
%28remainder%29%2F%28divisor%29 to the quotient:

3x%2B0%2B%28x-1%29%2F%28x%5E2%2B0x%2B1%29

Now we can drop the place holder zeros and get:

3x%2B%28x-1%29%2F%28x%5E2%2B1%29

Edwin