Question

Find the quotient using long division: (12a³-6a²-2a+7)/(4a+2)

Answer 1

The quotient of (12a³-6a²-2a+7) divided by (4a+2) is found using long division, where you divide the leading terms and subtract the product of the divisor and the result from the numerator, and repeat until the degree of the remainder is less or until there is no remainder.

Step-by-step explanation:

To find the quotient using long division for the expression (12a³-6a²-2a+7)/(4a+2), we follow these steps:

1. Divide the first term of the numerator by the first term of the denominator: 12a³/4a which gives us 3a².
2. Multiply the entire divisor (4a+2) by 3a² and subtract this from the numerator.
3. Repeat the division for the new, lower degree polynomial that appears after the subtraction.
4. Continue until the degree of the remainder is less than the degree of the divisor or until there is no remainder.

By carrying out the long division, you will find your quotient.