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Test3 M

This document is a test for the MHF4U1 - Unit 3 on Polynomial Functions, consisting of various questions that assess knowledge, application, and inquiry skills related to polynomial properties, division, factoring, graphing, and polynomial equations. It includes tasks such as determining properties of a given polynomial function, performing polynomial division, and analyzing graphs. Additionally, it features questions on local maxima and minima, as well as a table to complete regarding polynomial functions.

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Andy Shen
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47 views4 pages

Test3 M

This document is a test for the MHF4U1 - Unit 3 on Polynomial Functions, consisting of various questions that assess knowledge, application, and inquiry skills related to polynomial properties, division, factoring, graphing, and polynomial equations. It includes tasks such as determining properties of a given polynomial function, performing polynomial division, and analyzing graphs. Additionally, it features questions on local maxima and minima, as well as a table to complete regarding polynomial functions.

Uploaded by

Andy Shen
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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NAME: ___________________________

42 KNOW / 12 APP / 12 INQ / 12 COMM /6

MHF4U1 - UNIT 3 – POLYNOMIAL FUNCTIONS


TEST

1) For the function f ( x)  5( x  3)(2 x  5)( x  4) 2 , state the following properties.
(K – 6 marks)

a) Degree: _______ b) Leading coefficient: ________

c) Zeros: ________________________ d) Number of turning points: _________

e) End behaviour:

2) Divide (6 x 3  11x 2  9)  (2 x  1) . 3) Divide (3 x 4  2 x 3  3 x 2  5 x  8)  ( x 2  3 x  1) .


(K – 3 marks) (K – 3 marks)
4) Factor 2 x 4  x 3  23 x 2  46 x  24 . (A – 4 marks)

5) Factor 40 x 5  135 x 2 . (A – 3 marks)

6) For the graph of a polynomial function shown on the right, state


whether the leading coefficient of the polynomial is positive or
negative, and whether its degree is even or odd. (K – 2 marks)

Sign of leading coefficient: _____________

Degree even or odd: __________________

7) The graph on the left was obtained by transforming the graph of


y  x 3 . Determine the equation of the graph. (A – 3 marks)
8) Sketch the graph of f ( x)  x 4  4 x 3  20 x 2  48 x using the zeros and end behaviour. Be
sure to show all calculations. (I – 6 marks)

9) Determine the equation of the degree 6 polynomial


shown on the right. You may leave your answer in
factored form. (I – 3 marks)
10) The function f ( x)  ax 3  bx 2  116 x  30 has a factor of x – 3. Furthermore, when f(x) is
divided by x + 1, the remainder is 96. Determine the values of a and b. (I – 3 marks)

11) A student named Polly Nomial claimed that the function f ( x)  3(2 x  4) 7  1 has local
maxima and minima. Is Polly’s claim correct? Explain. (C – 2 marks)

12) Complete the following table. (C – 4 marks)


Type of Polynomial Minimum Number Maximum Number Minimum Number Maximum Number
Function of Zeros of Zeros of Turning Points of Turning Points

Cubic

Quartic

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