Synthetic Division

In this lesson, we will look at Synthetic Division, which is simplified form of long division.

Synthetic Division is an abbreviated way of dividing a polynomial by a binomial of the form (x + c) or (x – c). We can simplify the division by detaching the coefficients.

Example:

Evaluate (x³ – 8x + 3) ÷ (x + 3) using synthetic division

Solution:

(x³– 8x + 3) is called the dividend and (x + 3) is called the divisor.

Step 1:

Write down the constant of the divisor with the sign changed
–3

Step 2:

Write down the coefficients of the dividend. (Remember to add a coefficient of 0 for the missing terms)

Step 3:

Bring down the first coefficient.

Step 4:

Multiply (1)( –3) = –3 and add to the next coefficient.

Repeat Step 4 for all the coefficients

We find that (x³– 8x + 3) ÷ (x + 3) = x² – 3x + 1

Videos

It is easier to learn Synthetic Division visually. Please watch the following videos for more examples of Synthetic Division.

Using synthetic division with polynomials - Professor Edward Burger explains using synthetic division with polynomials

More synthetic division - Professor Edward Burger explains more synthetic division.

Synthetic Division – This video shows how to use synthetic division to divide a polynomial by a linear expression and also how to use the remainder to evaluate the polynomial.

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