Solving Polynomial Equations

Solving polynomial equations is equivalent to finding the y-intercepts of a polynomial equation.
If y = x^3-4x^2+8x-32 then to solve 0 = x^3-4x^2+8x-32 is the same as finding the x values that make y = 0. Here are two examples multiple times:

Rational functions - Oblique Asymptotes

In visible random groups we explored rational functions where the degree of the numerator is one more than the degree of the denominator. For example, a cubic divided by a quadratic.

Before we did this we recalled factoring a polynomial using the area model. My work and some other groups work.

 Then we reviewed a rational function with y = 0 as the horizontal asymptote. Degree of numerator is less than degree of denominator. Two examples.



Then we reviewed a rational function where with a horizontal asymptote of y = some number other than zero. Degree of Numerator = Degree of Denominator. Horizontal asymptote is y = (Leading Coefficient of Numerator) / (Leading Coefficient of the Denominator).

Then we looked at Rational Functions where the degree of the numerator is one more than the degree of the denominator. This creates an oblique asymptote.

Example 1

 Example 2

 Example 3

 Example 4

 

 

Example 5



 Example 6

 



Factoring Polynomials and Dividing Polynomials

We started by factoring a quadratic without any instruction. Here are some photos of student work and my work. Some used a "short cut" and others used area = length * width.



 

Next we divided a cubic by a linear function.