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Long Division & Synthetic Division Examples and Explanations

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Created on November 23, 2024

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Transcript

Long Division vs. Synthetic Division - All in One

Long Division & Synthetic Division You will find various problems and solutions so you can practice and check

Division Terms

Quotient

Divisor

Remainder

Dividend

Synthetic Division

  • Is a shortcut for long division
  • Only works if the divisor is linear

Linear. Can use synthetic division

Not Linear. Would need to use long division!

Intro to Synthetic Division

Understand this before moving on

Try it!

Try answering the problem below check your answer

Use Synthetic Division

Is it a factor?

If there is no remainder this means the divisor is a factor of the dividend.

Is a remainder so (x+2) is not a factor

no remainder so (x-3) is a factor

What if there is a coefficient in the divisor?

Try it!

Try answering the problem below check your answer

Use Long Division

Try it!

Try answering the problem below check your answer

Use Synthetic Division

Complex Synthetic Division

This video shows division by a trinomial using synthetic division - welcome to Algebra 2 advanced

Polynomial Division Recap!

Notes Page

Synthetic Division Recap!

Notes Page

Complete problems and check your answers!

Notes Page
Use Long Division

Complete problems and check your answers!

Notes Page
Use Long Division

Complete problems and check your answers!

Notes Page
Use Long Division

Complete problems and check your answers!

Notes Page
Use Synthetic Division

Complete problems and check your answers!

Notes Page
Use Synthetic Division

Complete problems and check your answers!

Notes Page
Use Synthetic Division

Below is a help video if needed! You are now an expert!

Notice that the divisor is a binomial with a coefficient that is not 1. Could you do synthetic division? Yes. You would divide by positive 1/4 and when you finish the process, you would have to divide by 4 (see next page)

Divide by positive 1/4 and when you finish the process, you would have to divide by 4 - one extra step! We often prefer long division if our divisor is a bit more complex than a linear binomial with a coefficient of 1.

For this problem, we could have easily factored but it is nice to see how one can do long division when a problem might be difficult to factor.