MATH 12 Virtual High School Unit 3 Pre Calculus Questions

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DESK Pre-Calculus Math 12
Unit 3
On-Line Course
SEND – IN ASSIGNMENT
UNIT 3
Polynomials
Name: _________________________________________
Teacher:________________________________________
If you are cross enrolled, state your other school besides DESK.
_________________________________________
Date that you submitted this assignment:
_________________________________________

You must show ALL work to receive full credit for the questions.
Total ______
=
_________%
50
SHOW ALL WORK FOR FULL MARKS
2017
Page 1 of 8
Unit 3
DESK Pre-Calculus Math 12
Unit 3
On-Line Course
1. Use long division to determine the remainder and the quotient for:
(3𝑥 3 − 2𝑥 2 + 7) ÷ (𝑥 + 2)
1) _____________________________
3 marks
2. Use synthetic division to determine remainder and quotient for:
(4𝑥 5 − 10𝑥 4 − 9𝑥 2 + 2) ÷ (𝑥 − 3)
2) _____________________________
3 marks
2017
Page 2 of 8
Unit 3
DESK Pre-Calculus Math 12
Unit 3
On-Line Course
3. Use synthetic division to solve for k. When 𝑥 3 + 𝑘 𝑥2 − 2𝑥 − 7 is divided by (𝑥 − 2) the remainder is 17. What is
the remainder when it is divided by (𝑥 + 1)?
3) _____________________________
2 marks
4. For 𝑃(x) = 2 𝑥 4 − 3𝑥 3 + 5𝑥2 − 7 determine P(2)
4) _____________________________
1 mark
5. Find the remainder when 𝑥 17 − 3𝑥 11 + 5 is divided by (𝑥 + 1).
5) _____________________________
1 mark
6. Given 𝑃(𝑥) = 3𝑥 4 + 4𝑥 3 − 3𝑥2 − 3𝑥 − 10. Is (𝑥 + 2) a factor of P(x)?
6) _____________________________
1 mark
2017
Page 3 of 8
Unit 3
DESK Pre-Calculus Math 12
Unit 3
On-Line Course
7. Use the remainder theorem to solve for k and m.
a)
When 3𝑥 4 + 𝑘𝑥2 + 7𝑥 + 9 is divided by (𝑥 + 2) , the remainder is 19.
7a) _____________________________
2 marks
b)
When 𝑘𝑥 3 + 𝑚𝑥2 + 𝑥 − 6 is divided by (𝑥 − 2), the remainder is 24. When this polynomial is divided by
(𝑥 + 1), the remainder is negative 15.
7b) _____________________________
3 marks
8.
According to the Rational Zero Theorem, list all possible rational roots of
𝑃(𝑥) = 3𝑥2 + 5𝑥 − 12
8) _____________________________
2 marks
2017
Page 4 of 8
Unit 3
DESK Pre-Calculus Math 12
9.
Unit 3
On-Line Course
Use an algebraic method to factor each of the following completely and find the zeros.
a) 𝑓(𝑥) = 3𝑥 3 + 7𝑥2 − 4
a) _____________________________
3 marks
b) 𝑓(𝑥) = 4𝑥 3 + 12𝑥2 + 5𝑥 − 6
b) _____________________________
3 marks
10. If 2 is a root of the equation 3𝑥 3 + 𝑥 2 − 20𝑥 + 12 = 0, determine the other roots.
10) ___________________________
2 marks
2017
Page 5 of 8
Unit 3
DESK Pre-Calculus Math 12
Unit 3
On-Line Course
11. A box is constructed such that the length is twice the width and the height is 4 cm longer than the width, with a
volume of 720 cm3. Find the dimensions of the box.
11) _____________________________
4 marks
12. An open top box is made from a piece of cardboard measuring 12 in x 15 in. Cutting out squares from each corner
and folding the edges up makes a box with a volume of 162 in3. How large a square must be cut from each corner? (Hint:
the answer is a rational number.)
12) _____________________________
4 marks
2017
Page 6 of 8
Unit 3
DESK Pre-Calculus Math 12
Unit 3
On-Line Course
13. Sketch the graph of each polynomial function without a calculator. Clearly show the zeros and
the y-intercept. Show algebraically how you determined the zeros and y-intercept.
a) 𝑓(𝑥) = 𝑥 3 + 2𝑥 2 − 11𝑥 − 12
y
x
3 marks
b) 𝑓(𝑥) = −𝑥 4 + 5𝑥 3 + 4𝑥 2 − 44𝑥 + 48
y
x
3 marks
2017
Page 7 of 8
Unit 3
DESK Pre-Calculus Math 12
Unit 3
On-Line Course
14. Use your graphing calculator to determine the following for the polynomial function:
𝑓(𝑥) = −𝑥 3 − 4𝑥2 + 5𝑥 + 11 (10 marks)
a) Domain
a) _____________________________
b) Range
b) _____________________________
c) The zeros
c) _____________________________
d) Y-intercept
d) _____________________________
e) coordinates of relative maximum
e) _____________________________
f) coordinates of relative minimum
f) _____________________________
g) intervals where f  x   0
g) _____________________________
h) intervals where f  x   0
h) _____________________________
i) what is the start and end behavior
i) _____________________________
2017
Page 8 of 8
Unit 3