long division

3x^2+8x+4/x+2=

http://www.sosmath.com/algebra/factor/fac01/fac01.html

To perform long division with polynomials, follow these steps:

Step 1: Set up the division in long division format, with the dividend (3x^2 + 8x + 4) inside the long division symbol and the divisor (x + 2) outside. Write the answer space above the long division symbol.

__________________
x + 2 | 3x^2 + 8x + 4

Step 2: Determine how many times the divisor (x + 2) can be divided into the first term of the dividend (3x^2). In this case, it can be divided 3x times. Write this value above the long division symbol as the first term of the quotient.

3x
__________________
x + 2 | 3x^2 + 8x + 4

Step 3: Multiply the divisor (x + 2) by the first term of the quotient (3x), and write the result below the dividend. Subtract this result from the dividend, and write the new result below the line.

3x
- (3x^2 + 6x)
__________________
x + 2 | 3x^2 + 8x + 4
- (3x^2 + 6x)
-----------
+ 2x + 4

Step 4: Bring down the next term of the dividend (- 2x + 4), and append it to the result.

3x
__________________
x + 2 | 3x^2 + 8x + 4
- (3x^2 + 6x)
-----------
2x + 4
+____________

Step 5: Determine how many times the divisor (x + 2) can be divided into the new dividend (2x + 4). In this case, it can be divided 2 times. Write this value as the second term of the quotient, below the first term.

3x + 2
__________________
x + 2 | 3x^2 + 8x + 4
- (3x^2 + 6x)
-----------
2x + 4
+____________


Step 6: Multiply the divisor (x + 2) by the second term of the quotient (2), and write the result below the last line. Subtract this result from the last line to find the remainder. If the remainder is zero, the division is complete. Otherwise, continue to the next step.

3x + 2
__________________
x + 2 | 3x^2 + 8x + 4
- (3x^2 + 6x)
-----------
2x + 4
- (2x + 4)
-----------
0

Step 7: The quotient is the sum of the quotient terms and the remainder.

Quotient: 3x + 2
Remainder: 0

So, the result of the long division is: 3x + 2.