Here’s a question to consider tonight. This question can be answer in much the same way as the inequalities we considered in class today (there is one minor difference—see if you can figure this out!).

Solve the inequality \(\displaystyle{\frac{x+1}{x-4}\leq \frac{1}{x-2}}\).

Factors, Roots, and the Fundamental Theorem of Algebra

We’ve now covered a number of important theorems concerning polynomials. For our next lesson complete the questions below.

Complete pages 124–125, questions 6, 11, 18, 22, 24, 26, 27, 32, 33, 34

In addition to these questions, if you’re ready for a challenge, try to answer any of the questions shown in the Polynomials Super Challenge. These are not assigned as homework, but if you can correctly complete question 1 you’ll get 1 bonus mark on our next test, and if you can correctly complete question 2 you’ll get 2 bonus marks on our next test. You have until the date of our next test to complete any of these challenge questions. Good luck!

Working with the Factor Theorem

Below is the question we considered at the end of our lesson today. Complete this question for our next lesson.

Let \(p(x)=2x^3+ax^2-29x+60\). The polynomial \(p\) is divisible by \((x-3)\).

a) Find \(a\).

b) \(-4\) is also a zero of \(p\). Find the third zero of \(p\).

Quadratics + Rational Functions Homework Assignment

Complete the questions in the file attached here and submit your work electronically (as a PDF).

Your file should be received before the beginning of our lesson on Sunday, November 13th. Note that the two bonus questions are optional, but I would encourage everyone to try at least one!

As always, you can write any questions you have about the assignment below in the comments section.

Quadratics + Even and Odd Functions

For tomorrow’s lesson complete the following questions.

Pages 110–112 questions 28, 30, 31, 43

Also, see if you can answer the following question: Is the sum of two odd functions always an even function? (And similarly, is the sum of two odd functions always an odd function?)