# How do you find the quotient of #(4y^2+8y+3)div(y+2)# using long division?

The remainder is

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To find the quotient of (4y^2+8y+3) divided by (y+2) using long division, follow these steps:

- Divide the first term of the dividend (4y^2) by the first term of the divisor (y). The result is 4y.
- Multiply the entire divisor (y+2) by the quotient obtained in step 1 (4y). The result is 4y^2+8y.
- Subtract the product obtained in step 2 from the dividend (4y^2+8y+3) to get the remainder. The remainder is -5y+3.
- Bring down the next term from the dividend (-5y) and divide it by the first term of the divisor (y). The result is -5.
- Multiply the entire divisor (y+2) by the quotient obtained in step 4 (-5). The result is -5y-10.
- Subtract the product obtained in step 5 from the remainder (-5y+3) to get the new remainder. The new remainder is 13.
- Since there are no more terms to bring down, the division is complete.
- The quotient is the sum of the quotients obtained in steps 1 and 4. Therefore, the quotient is 4y-5.

The quotient of (4y^2+8y+3) divided by (y+2) using long division is 4y-5.

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