Question

Use long division to divide. Divisor $x+3$ Dividend $$2x^2+10x+12$$

Short answer

By dividing $2x^2+10x+12$ by $x+3$, the result is $2x+4$. There is no remainder.

Step-by-step solution

Setup the Division

Set up the long division similarly to how numerical long division is set. Write the dividend $2x^2+10x+12$ inside the division symbol and the divisor $x+3$ outside the division symbol.

Divide the Leading Terms

Divide the first term of the dividend, $2x^2$, by the first term of the divisor, $x$. The result is $2x$, which is written on top of the division symbol.

Multiply Back and Subtract

Multiply the divisor $x+3$ by $2x$ from the result of the division above, giving $2x^2+6x$. Write this under the dividend and proceed to subtract $2x^2+6x$ from $2x^2+10x+12$.

Bring Down the Next Term

After subtracting, bring down the next term from the dividend. Here you'll have $4x+12$ in this case.

Continue the Division

Repeat the process for the next term. Divide the new first term of the dividend $4x$ by the first term of the divisor $x$, to yield $4$. Write this result above the division symbol, next to $2x$. Then multiply back, subtract and check if there are still terms from the dividend to bring down.

Repeat until Remains can't be Divided

Continue the process until all terms from the dividend are used up or what remains of the dividend after subtraction can't be divided by the divisor anymore. What remains is the remainder of the division.

Write the Final Result

The final result contains the quotient and the remainder (if any). Write down the solution in the format Quotient + Remainder/Divisor.