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Synthetic Division

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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 (xc). We can simplify the division by detaching the coefficients.


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


(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

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

synthetic division example

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


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

Polynomial Division: Synthetic Division
Perform synthetic division to divide by a binomial in the form (x - k)
Divide using synthetic division
1. (2x3 + 6x2 + 29) ÷ (x + 3)

2. (2x3 + 6x2 - 17x + 15) ÷ (x + 5)

3. (y5 - 32) ÷ (y - 2)

4. (16x3 - 2 + 14x - 12x2) ÷ (2x + 1)
Divide a Trinomial by a Binomial Using Synthetic Division
Divide using synthetic division
1. (x2 - 5x + 7) ÷ (x - 2)

2. (x2 + 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.
(x3 - 2x2 + 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.
(x4 - x2 + 5) ÷ (x + 3)

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