long division polynomial?

Question

how do you divide x^2/2x + 4 ?
can you explain step by step.

Answer 1

½x - 1 R 4

Set it up like the long division you learned for numbers with x^2 + 0x + 0 under the division bar. Then put whatever you have to multiply the "2x" in 2x + 4 by to get 1x^2: ½x. Do the multiplication placing terms under the x^2... in their proper places: you then have (x^2 + 0x) - (x^2 + 2x) = -2x. Put the "-2x" under the x column and then put above the 0 the number you have to multiply the "2x" in 2x + 4 by to get -2x: -1. Do the multiplication and subtraction: you get 4. You stop when you reach the x^0 term (4x^0 = 4). Anything left (number only) is the remainder. So your answer is: ½x - 1 R 4.

Answer 2

I haven't checked the answer, but hopefully you can get the method.

___
2x + 4)x^2

Put a term up on the top such that when you multiply 2x + 4 by it it will give x^2.

0.5x
2x + 4)x^2

Multiply 2x + 4 by this and put it underneath.

0.5x
2x + 4)x^2
x^2 + 2x

Change the signs of the bit you just did.

0.5x
2x + 4)x^2
-x^2 - 2x

Sum this. The first bit will obviously be 0 because you chose that walue to be that.

0.5x
2x + 4)x^2
-x^2 - 2x
0 - 2x

Now add a term that will give a product equalling -2x.

0.5x - 1
2x + 4)x^2
-x^2 - 2x
0 - 2x

Multiply by this and add to the bottom line. Bring down the next term from the numerator (in this case 0)

0.5x - 1
2x + 4)x^2 + 0x + 0
-x^2 - 2x
0 - 2x + 0
-2x - 4

Change signs


0.5x - 1
2x + 4)x^2
-x^2 - 2x
0 - 2x
2x + 4
0 + 4

So you have 0.5x - 1, remainder 4. This 4 is still being divided by the original denominator, so

0.5x - 1 + 4/(2x + 4)

Answer 3

x^2 / 2x + 4

first write x^2 as x^2 + 0x + 0

how many times does 2x go into x^2? (1/2)x times right?

put (1/2)x in the quotient area.

next multiply 2x + 4 through by (1/2)x. you get x^2 + 2x.

change the signs in order to subtract. you get -2x + 0 (bring down the 0 from the dividend)

how many times does 2x go into -2x? 1 time, right?

put -1 in the quotient area next to the first term which is (1/2)x.

multiply 2x + 4 through by -1. you get -2x + 4

change the signs in order to subtract. you get -4.

since you cannot divide any further, your answer is (1/2)x - 1, remainder 4.

Answer 4

x²/(2x + 4)
By long division:

2x + 4)x² + 0x + 0
...........---------------
.......... x² + 2x ....(½x
..........-----------
...........0x² - 2x + 0(-1
................ -2x - 4
.................-----------
..................0x + 4

So x²/(2x + 4) = ½x - 1 + 4/(2x + 4)
= ½x - 1 + 2/(x + 2)

OR if you prefer
x² = (2x + 4)(½x - 1) + 4