SOLUTION: long division: (x^3-3x^2+2x-8)/(x^2+4) and find the 9th term of: (x^2-2)^9 I need help i'm completely confused on long division and terms. I don't understand the formulas.

Algebra ->  Sequences-and-series -> SOLUTION: long division: (x^3-3x^2+2x-8)/(x^2+4) and find the 9th term of: (x^2-2)^9 I need help i'm completely confused on long division and terms. I don't understand the formulas.       Log On


   

Question 1060705: long division: (x^3-3x^2+2x-8)/(x^2+4)
and find the 9th term of:
(x^2-2)^9
I need help i'm completely confused on long division and terms. I don't understand the formulas. Can you help?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The second question is reliant on simply following the Binomial Theorem. You can refer to that and fill-in what you need.

The long division for the polynomials works the same way as long division for regular base-ten numbers, and can be done without the condensing that you would be able if in base-ten numbers.

This could be broken into steps with explanations, but here I will just show the whole thing in one finished piece:

The dividend is shown toward the right, and the divisor is shown at the left, and you begin first asking, what is x^3 divided by x^2; and this is x; and so you put in the first partial quotient of x, ABOVE the x^3.

       |_______________________________________
x^2+4  |    x^3    -3x^2    +2x      -8
       |
       |
       |_________________

You need to observe that the divisor has a term, 0%2Ax and you should account for this term when performing the partial multiplications .

             x      -3
       |_______________________________________
x^2+4  |    x^3    -3x^2    +2x      -8
       |
       |    x^3    0x^2     4x
       |_________________
            0      -3x^2    -2x     -8
                   -3x^2     0x     -12
                  _______________________
                    0        -2x    4

The quotient is x-3 and the remainder is -2x%2B4.

The entire quotient with the remainder can also be expressed according to its complete meaning, x-3%2B%28-2x%2B4%29%2F%28x%5E2%2B4%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
long division: (x^3-3x^2+2x-8)/(x^2+4)
and find the 9th term of:
(x^2-2)^9
I need help i'm completely confused on long division and terms. I don't understand the formulas. Can you help? 


The formula you need for the 9th term of a BINOMIAL EXPANSION is: , where, in this case:

a = x%5E2

b = - 2

n = 9

r, or term number = 9



Therefore,  becomes: 





It is that easy....nothing too COMPLEX!