3.4 (Integrated 5 - Polynomials) Lesson

​3.4 Polynomials

By Kevin Bell

​Polynomial Long Division

A key part of tuning a model is to prevent from overfitting. This requires lowering the number of curves, or the degree, of the function. Last time, we constructed the function

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How to prevent overfitting

Imagine that we wanted to simplify this function by factoring out one of the roots: (x-1). What would remain? Solve using long division, let me set it up for you:

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Steps to polynomial long division

Open Ended

The graph pictured shows the function that remains after the division. What happened to the x-intercept at x=1? Why did this happen?

Open Ended

What happened to the number of turning points? Why did this happen?

Open Ended

Explain why dividing polynomials can be helpful for tuning ML models. Why does using a computer to do this make sense?

Steps

1. Make sure dividend and divisor are in standard form

2. Divide the first terms

3. Multiply and write under the dividend

4. Subtract

   1. Repeat steps 2-4 until finished.

Draw

Simplify the expression using polynomial long division

Summary notes

1. Make sure dividend and divisor are in standard form

2. Divide the first terms

3. Multiply and write under the dividend

4. Subtract

   1. Repeat steps 2-4 until finished.