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Teacherbot 30 Jul, 05:57:03

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 + 2). _________ x + 1 | 3x^2 + 5x + 2 - (3x^2 + 3x) _______ 2x + 2

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

Step 6: Multiply the result obtained in step 5 (2) by the divisor (x + 1). The result is 2x + 2. _________ x + 1 | 3x^2 + 5x + 2 - (3x^2 + 3x) _______ 2x + 2 - (2x + 2) _______ 0

Step 7: Since there are no more terms to bring down and divide, 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, follow these steps: 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. 6. Repeat steps 2-5 until there are no more terms to bring down. 7. The quotient is the result obtained from the division, and the remainder is the final expression after all terms have been divided.

You 30 Jul, 05:59:27

Make this simpler to understand

Teacherbot 30 Jul, 05:59:27

Sure! Here’s a simplified explanation of division of algebraic expressions:

  1. Start by arranging the expressions in the division format, with the divisor on the outside and the dividend on the inside.

  2. Divide the first term of the dividend by the first term of the divisor. This gives you the first term of the quotient.

  3. Multiply the first term of the quotient by the divisor. This gives you a new expression.

  4. Subtract the new expression from the dividend.

  5. Bring down the next term from the dividend.

  6. Repeat steps 2-5 until there are no more terms to bring down.

  7. The quotient is the result obtained from the division, and the remainder is the final expression after all terms have been divided.

Remember to simplify the quotient and remainder if possible.

Let’s use an example to illustrate this:

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

Step 1: Arrange the expressions: (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.

Step 3: Multiply 3x by the divisor (x + 1). The result is 3x^2 + 3x.

Step 4: Subtract 3x^2 + 3x from the dividend: (3x^2 + 5x + 2) - (3x^2 + 3x) = 2x + 2.

Step 5: Bring down the next term from the dividend: 2x + 2.

Step 6: Divide 2x by x. The result is 2.

Step 7: Multiply 2 by the divisor (x + 1). The result is 2x + 2.

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

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

I hope this explanation is simpler to understand! Let me know if you have any further questions.