Determine the first term of the quotient by dividing the leading term of the dividend by the leading term of the divisor. Multiply the answer by the divisor and write it below the like terms of the dividend. Subtract the bottom binomial from the terms above it. Bring down the next term of the dividend.

How To: Given two polynomials, use synthetic division to divide

1. Write k for the divisor.
2. Write the coefficients of the dividend.
3. Bring the leading coefficient down.
4. Multiply the leading coefficient by k. …
5. Add the terms of the second column.
6. Multiply the result by k. …
7. Repeat steps 5 and 6 for the remaining columns.

To solve a polynomial equation, first write it in standard form. Once it is equal to zero, factor it and then set each variable factor equal to zero. The solutions to the resulting equations are the solutions to the original. Not all polynomial equations can be solved by factoring.

Long Division Steps

1. Step 1: Take the first digit of the dividend from the left. …
2. Step 2: Then divide it by the divisor and write the answer on top as the quotient.
3. Step 3: Subtract the result from the digit and write the difference below.
4. Step 4: Bring down the next digit of the dividend (if present).

The advantages of synthetic division are that it allows one to calculate without writing variables, it uses few calculations, and it takes significantly less space on paper than long division.