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More Lessons for Algebra

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

### What is Synthetic 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.

### Videos

**Polynomial Division: Synthetic Division**

Perform synthetic division to divide by a binomial in the form (x - k)

Example:

Divide using synthetic division

1. (2x^{3} + 6x^{2} + 29) ÷ (x + 3)

2. (2x^{3} + 6x^{2} - 17x + 15) ÷ (x + 5)

3. (y^{5} - 32) ÷ (y - 2)

4. (16x^{3} - 2 + 14x - 12x^{2}) ÷ (2x + 1)

**Divide a Trinomial by a Binomial Using Synthetic Division**

Example:

Divide using synthetic division

1. (x^{2} - 5x + 7) ÷ (x - 2)

2. (x^{2} + 8x + 12) ÷ (x + 2)

**Synthetic Division**
This video shows how you can use synthetic division to divide a polynomial by a linear expression.

It also shows how synthetic division can be used to evaluate polynomials.

Example:

(x^{3} - 2x^{2} + 3x - 4) ÷ (x - 2)

**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.

Example:

(x^{4} - x^{2} + 5) ÷ (x + 3)

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Algebra

Math Worksheets

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 (

**Example:**

Evaluate (*x*^{3} – 8*x* + 3) ÷ (*x* + 3) using synthetic division

**Solution:**

(*x*^{3}– 8*x* + 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 (*x*^{3}– 8*x* + 3) ÷ (*x* + 3) = *x*^{2} – 3*x* + 1

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

Perform synthetic division to divide by a binomial in the form (x - k)

Example:

Divide using synthetic division

1. (2x

2. (2x

3. (y

4. (16x

Example:

Divide using synthetic division

1. (x

2. (x

It also shows how synthetic division can be used to evaluate polynomials.

Example:

(x

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.

Example:

(x

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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