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More Lessons for Algebra

Math Worksheets

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)

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

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