In these lessons, we will look at Synthetic Division, which is simplified form of long division.
Related Pages
Long Division Of Polynomials
More Lessons for Algebra
Math Worksheets
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 (x^{3} – 8x + 3) ÷ (x + 3) using synthetic division
Solution:
(x^{3}– 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 (x^{3}– 8x + 3) ÷ (x + 3) = x^{2} – 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)
Example:
Divide using synthetic division
(2x^{3} + 6x^{2} + 29) ÷ (x + 3)
(2x^{3} + 6x^{2} - 17x + 15) ÷ (x + 5)
(y^{5} - 32) ÷ (y - 2)
(16x^{3} - 2 + 14x - 12x^{2}) ÷ (2x + 1)
Divide a Trinomial by a Binomial Using Synthetic Division
Example:
Divide using synthetic division
(x^{2} - 5x + 7) ÷ (x - 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)
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