Another Fun round of Math!

I know math is not the fun class but I am really enjoying study the subject this year, within 2018 – 2019 I got to learn about Precalculus, which includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus. Ever thought, algebra and trigonometry is not my strength I still want to build those skill into my strength. This round we are studying in Chapter 3 (Polynomial and Rational Functions), which include seven smaller subjects. I would like to show some example in the small subjects that related to Chapter 3.

In Chapter 3.2 (Polynomial Functions and Their Graphs) we learn the polynomial functions simply as *polynomials. *The following polynomial has degree 5 leading coefficient 3, and constant term -6

We also need to understand how the graph of a basic polynomial function look like and which graph is not a polynomial function.

Example: P(x)=x^4 − x^3 − 6x^2

First, we’ll need to factor this polynomial as much as possible so we can identify the zeros and get their multiplicities.

P(x )= x^4 − x^3 − 6x^2 = x^2(x^2 − x − 6) = x^2(x − 3)(x + 2)

Here is a list of the zeroes and their multiplicities.

X = −2 (multiplicity 1)

X = 0 (multiplicity 2)

X = 3 (multiplicity 1)

So, the zeros at x = -2 and x = 3 which will correspond to x-intercepts, that cross the x-axis since their multiplicity is odd. The zero at x = 0 will not cross the x-axis since it multicity is even. The y-intercept is (0,0) and notices that this is also an x-intercept.

The coefficient of the 4th-degree term is positive and so since the degree is even we know that the polynomial will have a positive infinite bound at both ends of the graph.

Finally, here are some function that helps to the graph, We need to plug in a random number to help identify the behavior of the graph. Normally, we would have one point in between the zeros.

P(−3) = 54

P(−1) = −4

P(1) = −6

P(4) = 96

Here is a sketch of a graph