Division of algebraic expressions is the process of dividing one algebraic expression by another. It involves dividing the coefficients and dividing the variables with the same exponents.

To understand division of algebraic expressions, let’s consider an example:

Divide (3x^2 + 5x + 2) by (x + 1).

Step 1: Arrange the expressions in the division format: ___________ x + 1 | 3x^2 + 5x + 2

Step 2: Divide the first term of the dividend (3x^2) by the first term of the divisor (x). The result is 3x. ___________ x + 1 | 3x^2 + 5x + 2 - (3x^2 + 3x)

Step 3: Multiply the result obtained in step 2 (3x) by the divisor (x + 1). The result is 3x^2 + 3x. _________ x + 1 | 3x^2 + 5x + 2 - (3x^2 + 3x) _______ 2x + 2

Step 4: Bring down the next term from the dividend (2x) and repeat steps 2 and 3. _________ x + 1 | 3x^2 + 5x + 2 - (3x^2 + 3x) _______ 2x + 2 - (2x + 2) _________ 0

Step 5: Since there are no more terms to bring down, the division is complete. The quotient is 3x + 2, and the remainder is 0.

Therefore, (3x^2 + 5x + 2) divided by (x + 1) is equal to 3x + 2.

In summary, to divide algebraic expressions: 1. Arrange the expressions in the division format. 2. Divide the first term of the dividend by the first term of the divisor. 3. Multiply the result obtained in step 2 by the divisor. 4. Subtract the result obtained in step 3 from the dividend. 5. Bring down the next term from the dividend and repeat steps 2 and 3. 6. Continue steps 4 and 5 until there are no more terms to bring down. 7. The quotient is the result obtained from the division, and the remainder is the remaining terms after the division is complete.