# How do you find the quotient #(3y^3+8y^2+y-7)div(y+2)# using long division?

#3y^2+2y-3#

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The quotient is

Let's perform the long division

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To find the quotient using long division, follow these steps:

- Divide the first term of the dividend (3y^3) by the first term of the divisor (y). The result is 3y^2.
- Multiply the entire divisor (y+2) by the quotient obtained in step 1 (3y^2). The result is 3y^3 + 6y^2.
- Subtract the product obtained in step 2 from the dividend (3y^3 + 8y^2 + y - 7). The result is 2y^2 + y - 7.
- Bring down the next term from the dividend (-7).
- Divide the first term of the new dividend (2y^2) by the first term of the divisor (y). The result is 2y.
- Multiply the entire divisor (y+2) by the quotient obtained in step 5 (2y). The result is 2y^2 + 4y.
- Subtract the product obtained in step 6 from the new dividend (2y^2 + y - 7). The result is -3y - 7.
- Bring down the next term from the dividend (-7).
- Divide the first term of the new dividend (-3y) by the first term of the divisor (y). The result is -3.
- Multiply the entire divisor (y+2) by the quotient obtained in step 9 (-3). The result is -3y - 6.
- Subtract the product obtained in step 10 from the new dividend (-3y - 7). The result is -1.
- There are no more terms to bring down, so the division is complete.
- The quotient is 3y^2 + 2y - 3, and the remainder is -1.

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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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