how to use synthetic division
Related Pages
Long Division Of Polynomials
More Lessons for Algebra
Math Worksheets
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.
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
Videos
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
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(2x3 + 6x2 + 29) ÷ (x + 3)
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(2x3 + 6x2 - 17x + 15) ÷ (x + 5)
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(y5 - 32) ÷ (y - 2)
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(16x3 - 2 + 14x - 12x2) ÷ (2x + 1)
- Show Video Lesson
Divide a Trinomial by a Binomial Using Synthetic Division
Example:
Divide using synthetic division
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(x2 - 5x + 7) ÷ (x - 2)
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(x2 + 8x + 12) ÷ (x + 2)
- Show Video Lesson
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:
(x3 - 2x2 + 3x - 4) ÷ (x - 2)
- Show Video Lesson
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:
(x4 - x2 + 5) ÷ (x + 3)
- Show Video Lesson
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how to use synthetic division
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