Polynomial Practice Test
Chapter
Chapter 2
Section
Polynomial Practice Test
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Solutions 32 Videos

Which statements is true?

\displaystyle P(x) = 5x^3 + 4x^2 -3x + 2 ?

A. When P(x) is divided by x+ 1, the remainder is 8.

B. x + 2 is a factor of P(x).

C. \displaystyle P(-2) = -16

D. \displaystyle P(x) = (x + 1)(5x^2 -x -2)-4

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Q1

Which of the following is not a factor of 2x^3 -5x^2 -9x + 18?

A. \displaystyle 2x -3

B. \displaystyle x + 1

C. \displaystyle x -2

D. \displaystyle x - 3

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Q2

Which set of values for x should be tested to determine the possible zeros of 4x^3 + 5x^2 -23x -6?

A. \displaystyle \pm 1, \pm2, \pm 3, \pm 4, \pm 6 $`

B. \displaystyle \pm 1, \pm 2, \pm3, \pm 4, \pm 6, \pm \frac{1}{2}, \pm \frac{2}{3}

C. \displaystyle \pm 4, \pm6, \pm \frac{1}{2}, \pm \frac{3}{2}, \pm \frac{3}{4}, \pm \frac{1}{4}

D. \displaystyle \pm 1, \pm 2, \pm 3, \pm 6, \pm \frac{1}{2}, \pm \frac{3}{2}, \pm \frac{3}{4}, \pm \frac{1}{4}

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Q3

a) Divide x^3 -4x^2+ 3x-7 by x + 3. Express the result in quotient form.

b) Identify any restrictions on the variable.

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Q4

a) Determine the value of k such that when f(x) = x^4 + kx^3 -2x^2 + 1 is divided by x + 2, the remainder is 5.

b) Determine the remainder when f(x) is divided by x +4

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Q5

Factor.

\displaystyle x^3 -5x^2 + 2x + 8

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Q6a

Factor.

\displaystyle x^3 + 2x^2 - 9x -18

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Q6b

Factor.

\displaystyle x^3 + 5x^2 - 2x -24

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Q6c

Factor.

\displaystyle 4x^3 + 7x^2 - 8x -4

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Q6d

Factor

\displaystyle x^3 + 9x^2 +26x + 24

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Q6e

Factor

\displaystyle 2x^4+13x^3 + 28x^2 + 23x + 6

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Q6f

Use the graph to determine the roots of the corresponding polynomial equation. Window variables: x \in [-8, 8], y \in[40,40], Yscl=4

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Q7

Determine the real roots of the equation.

\displaystyle (x^2 + 5)(x - 2) = 0

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Q8a

Determine the real roots of the equation.

\displaystyle (x^2 - 121)(x^2+ 16) = 0

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Q8b

Determine the real roots of the equation.

\displaystyle (x^2 -2x + 3)(2x^2 - 50) = 0

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Q8c

Determine the real roots of the equation.

\displaystyle (3x^2 -27)(x^2 -3x -10) = 0

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Q8d

Solve by factoring.

\displaystyle x^3 + 4x^2 + 5x + 2 = 0

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Q9a

Solve by factoring.

\displaystyle 32x^3-48x^2 -98x + 147 = 0

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Q9c

Solve by factoring.

\displaystyle 45x^4 -27x^3 -20x^2 + 12 x = 0

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Q9d

a) Describe the similarities and differences between polynomial equations, polynomial functions, and polynomial inequalities. Support your answer with examples.

b) What is the relationship between roots, zeros, and x—intercepts? Support your answer with examples.

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Q10

a) Determine an equation for the quartic function represented by this graph.

b) Use the graph to identify the intervals on which the function is below the x—axis.

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Q11

a) Determine an equation, in simplified form, for the family of quartic functions with Zeros 5 (Order 2) and -2 \pm \sqrt{6}.

b) Determine an equation for the member of the family whose graph has a y-intercept of 20.

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Q12

Boxes for chocolates are to be constructed from cardboard sheets that measure 36 cm by 20 cm. Each box is formed by folding a sheet along the dotted lines, as shown.

a) Express the volume of the box as a function of x.

b) Determine the possible dimensions of the box if the volume is to be 450 cm“. Round answers to the nearest tenth of a centimetre.

c) Write an equation for the family of functions that corresponds to the function in part a).

d) Sketch graphs of two members of this family on the same coordinate grid.

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Q13

Solve using technology.

x^3 +3x \leq 8x^2 - 9

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Q14a

Solve using technology.

-x^4 + 3x^3 + 9x^2 > 5x + 5

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Q14b

Solve using technology.

x^3 + 3x^2 -4x - 7 < 0

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Q15a

Solve using technology.

2x^4 + 5x^3 -3x^2 -15x -9 \geq 0

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Q15b

Solve by factoring.

\displaystyle 9x^2 - 16 < 0

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Q16a

Solve by factoring.

\displaystyle -x^3 + 6x^2 -9x > 0

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Q16b

Solve by factoring.

\displaystyle 2x^3 + 5x^2 -18x -45 \leq 0

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Q16c

Solve by factoring.

\displaystyle 2x^4 + 5x^3 -8x^2 -17x -6 \geq 0

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Q16d

A open top box is to be constructed from a piece of cardboard by cutting congruent squares from the corners and then folding up the sides. The dimensions of the cardboard are shown.

a) Express the volume of the box as a function of x.

b) Write an equation that represents the box with volume

  • i) twice the volume fo the box represented by the function in part a)
  • ii) half the volume of the box represented by the function in part a)

c) Use your function from part a) to determine the values of x that will result in boxes with a volume greater than 2016 cm^3.

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Q17