Division Polynomials
2x square + 4 /2x
2x^2 + 4/(2x) = 2 (x^2 + 1/x)
What are you dividing BY?
dividing by 2x
To divide the polynomial 2x^2 + 4 by 2x, you can use long division. Here's how:
1. Write the dividend (2x^2 + 4) and the divisor (2x) in long division format:
-----------------
2x | 2x^2 + 4
2. Divide the first term of the dividend by the first term of the divisor. In this case, (2x^2) ÷ (2x) = x. Write this result above the line as the first term of the quotient:
x
-----------------
2x | 2x^2 + 4
3. Multiply the divisor (2x) by the first term of the quotient (x), and write the result below the dividend:
x
-----------------
2x | 2x^2 + 4
- 2x^2
4. Subtract the result obtained in step 3 from the dividend:
x
-----------------
2x | 2x^2 + 4
- 2x^2
-------
4
5. Determine the next term of the quotient by dividing the result obtained in step 4 by the divisor. In this case, (4) ÷ (2x) = 2/x. Write this result above the line as the next term of the quotient:
x + 2/x
-----------------
2x | 2x^2 + 4
- 2x^2
-------
4
6. Now, multiply the divisor (2x) by the term (x + 2/x) in the quotient, and write the result below the dividend:
x + 2/x
-----------------
2x | 2x^2 + 4
- 2x^2
-------
4x
7. Subtract the result obtained in step 6 from the previous result (4x) to get the final remainder:
x + 2/x
-----------------
2x | 2x^2 + 4
- 2x^2
-------
4x
- 4x
--------
0
The final result is x + 2/x, and since there is no remainder, the division is exact.