# How do you find the quotient of #(3x^2 + 4xy + 3xy + 4y^2) ÷ (x + y)#?

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To find the quotient of (3x^2 + 4xy + 3xy + 4y^2) ÷ (x + y), we can use polynomial long division or synthetic division.

Using polynomial long division:

- Divide the first term of the dividend (3x^2) by the first term of the divisor (x). The result is 3x.
- Multiply the divisor (x + y) by the quotient obtained in step 1 (3x), and subtract the result from the dividend (3x^2 + 4xy + 3xy + 4y^2 - 3x(x + y)).
- Bring down the next term of the dividend (-3xy).
- Repeat steps 1-3 until all terms have been divided.
- The quotient is the sum of the quotients obtained in each step. In this case, the quotient is 3x - 3y.

Using synthetic division:

- Set up the synthetic division table with the divisor (x + y) as the divisor and write the coefficients of the dividend (3, 4, 3, 4) in descending order.
- Bring down the first coefficient (3) to the bottom row.
- Multiply the divisor (x + y) by the result obtained in step 2 (3), and write the product below the next coefficient (4).
- Add the two numbers in the bottom row (3 + 4 = 7), and write the sum below the next coefficient (3).
- Repeat steps 3-4 until all coefficients have been divided.
- The quotient is the set of numbers in the bottom row, which in this case is 3, 7, and -3.

Therefore, the quotient of (3x^2 + 4xy + 3xy + 4y^2) ÷ (x + y) is 3x - 3y.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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