My way of doing this is similar to traditional long division. The divisor goes to the left of the division bracket and the dividend goes inside the division bracket. When writing a binomial, every degree from the degree of the highest term to degree zero must be represented in a term. This means that is there is a degree in the polynomial that is not represented in a term, it must be filled in by writing a term in that degree with a coefficient of zero. So in this example, **t**^{2} - 13 should be written as **t**^{2} + 0t - 13. We need to do this because when we do the algorithm, we'll want all terms of the same kind to be perfectly lined up in columns all the way down to the finish.

So, to the left of the division bracket, write **t + 4**. Inside the division bracket, write **t**^{2} + 0t - 13.

**Divide** the first term of the dividend (**t**^{2}) by the first term of the divisor (**t**). The answer is **t**. Write the answer as the first term on top of the division bracket.

**Multiply** the answer (**t)** by the divisor (**t+4**). The answer is **t**^{2} + 4t. Write the answer under the dividend making sure that the terms of like degrees line up vertically. That means to write the **t**^{2} from the answer under the **t**^{2} in the dividend and write the **+4t** from the answer under the **+0t** of the dividend. Draw a horizontal line under the answer.

Since we wrote two terms as the answer, we will **subtract** them from the two terms above. So subtract **t**^{2} + 4t from **t**^{2} + 0t. The answer is **-4t**. Write the answer under the horizontal line making sure again to line up like terms.

Let's introduce the next term from the divisor to the algorithm below. **Bring down** the **-13** from the divisor and write it to the right of the **-4t** from the answer above. We now have a new dividend of **-4t - 13**.

You should start to see something familiar emerge. The old algorithm of **divide, multiply, subtract, bring down, and repeat** you remember from elementary long division should be obvious here.

Next, we will **divide** the first term of the new dividend (**-4t**) by the first term of the divisor (**t**). The answer is **-4**. Write the answer on top of the division bracket to the right of the **t** that we got from the last time we divided. The quotient should now say **t - 4**. This is the completed quotient, but we must press on to find the remainder.

**Multiply** the **-4** from the quotient on by the divisor (**t + 4**). The answer is **-4t - 16**. Write this under the new dividend (**-4t - 13**) making sure to line up like terms. draw a horizontal line under the answer.

Subtract the answer (**-4t - 16**) from the new dividend (**-4t - 13**). The answer is **3**. This is the remainder. Write the remainder under the horizontal line.

So **(t**^{2} -13) / (t + 4) = t - 4 with a remainder of **3**.