# Polynomials Quiz

## Web resources available

This quiz tests the work covered in Lecture 5 and corresponds to the first half of
Section 1.6 of the textbook Calculus: Single and Multivariable (Hughes-Hallett,
Gleason, McCallum et al.).

There are further web quizzes at Wiley. Choose section 6 from this page.

Be aware that it doesn’t seem to accept the written answers so you will have to check whether your answers are correct when they print the correct answer. Question 15 didn’t make sense on 7/11/05

You may wish to start reviewing the section on powers at
http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/zoo/powers.html and then
continue to http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/zoo/polynomials.html,
both pages have useful graphics.

You need to be able to expand and factorize quadratics so you may find
http://home.xnet.com/ fidler/triton/math/review/mat085/factor/factor1.htm useful
to review factoring.

There is a puzzle at http://www.univie.ac.at/future.media/moe/tests/fun1/erkennen.html which gets you to match quadratic and linear graphs to their formulae.

There are some java applets at http://id.mind.net/ zona/mmts/functionInstitute/polynomialFunctions/graphs/polynomialFunctionGraphs.html which let you play with the coefficients of polynomials of various degrees. This gives a very good idea of how the coefficients change the graph.

There is another function plotter at http://www.quickmath.com/ if you click on plot in equations. This site is very good so you may wish to explore other aspects as well.

## Question 1

$1{0}^{6}{x}^{2}$ dominates ${2}^{x}$ as $x\to \infty \phantom{\rule{0.3em}{0ex}}.$

**Not correct. Choice (a) is false.**

**Your answer is correct.**

## Question 2

**There is at least one mistake.**

For example, choice (a) should be true.

**There is at least one mistake.**

For example, choice (b) should be false.

**There is at least one mistake.**

For example, choice (c) should be false.

**There is at least one mistake.**

For example, choice (d) should be true.

**There is at least one mistake.**

For example, choice (e) should be true.

**There is at least one mistake.**

For example, choice (f) should be false.

**Your answers are correct**

**True**. The highest power of $x$ is 3 and this is degree of the polynomial and the coefficient of ${x}^{3}$ is 7 and this is the leading coefficient.**False**. Try again, read the definition of a polynomial on page 38.**False**. Try again, read the definition of a polynomial on page 38.**True**. The highest power of $x$ is 4 and this is degree of the polynomial and the coefficient of ${x}^{4}$ is -5 and this is the leading coefficient.**True**. In a polynomial the powers of $x$ must be positive.**False**. Try again, read the definition of a polynomial on page 38.

## Question 3

Which of the the following statements are correct?

**Not correct. Choice (a) is false.**

**Your answer is correct.**

**Not correct. Choice (c) is false.**

**Not correct. Choice (d) is false.**

## Question 4

**Your answer is correct.**

**Not correct. Choice (b) is false.**

**Not correct. Choice (c) is false.**

**Not correct. Choice (d) is false.**