Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Determine the product (x + 2)(x – 6).
a. | x2 – 12x – 12 | c. | x2 –
4x – 12 | b. | x2 + 2x –
12 | d. | x2
– 12x – 4 |
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2.
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Which of the following binomial multiplication expressions does the diagram
represent?  a. | (2x + 3)(x + 3) | c. | (3x + 3)(x +
3) | b. | (2x + 3)(x + 9) | d. | (3x + 3)(x +
9) |
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3.
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The greatest common factor (GCF) for the set of terms 30x, 45x,
60x2, and 30x2 is
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4.
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The expression –8x2 – 56x written in fully
factored form is
a. | –8x(x + 7) | c. | –8(x2 +
7x) | b. | –4x(2x + 14) | d. | –8(x2 –
7x) |
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5.
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What is the expression –66x2 + 24x + 18 in
factored form?
a. | –6(11x2 – 4x – 3) | c. | –6(11x2 + 4x + 3) | b. | –6(–11x2 + 4x + 3) | d. | –6(–11x2 –
4x – 3) |
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6.
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What is the factored form of the expression 5x2 –
55?
a. | 5x2(x – 11) | c. | 5x(x2
– 11) | b. | 5x(x – 11) | d. | 5(x2 –
11) |
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7.
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The area of a rectangular picture frame is represented by the equation A
= 6x2 – 15x. When the expression is factored fully, the factors are
the dimensions of the frame. What are the dimensions of the frame?
a. | 3 by 2x2 – 5 | c. | 3x by 2x –
5 | b. | 3 by 2x – 5 | d. | 3x2 by 2x – 5 |
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8.
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The area of a classroom door is represented by the equation A =
36z2 + 3600z. When the expression is factored fully, the factors are the
dimensions of the door. What are the actual height and width of the door if z = 5 cm?
a. | 180 cm by 105 cm | c. | 160 cm by 120 cm | b. | 170 cm by 100 cm | d. | 150 cm by 110
cm |
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9.
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Which of the following values of k makes the trinomial
36x2 + kx + 81 a perfect square?
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10.
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Which expression is an example of a difference of squares?
a. | x2 – 21 | c. | 9x –
64 | b. | 4x + 16 | d. | 25x2 – 81 |
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11.
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Which expression is not an example of a difference of squares?
a. | 225 – 100x2 | c. | 36x2 –
49 | b. | 64 – 16x2 | d. | 9x2 –
181 |
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12.
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Factor x2 – 400.
a. | (x + 20)(x – 20) | c. | (x + 20)(x +
20) | b. | (x – 20)(x – 20) | d. | cannot be
factored |
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13.
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Which value of k makes the trinomial x2 + 12x +
k a perfect square?
a. |  | c. | 36 | b. | 144 | d. | 18 |
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14.
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Suppose the area of a rectangle is represented by the expression
100x2 – 49. When the expression is fully factored, the factors represent the
dimensions of the rectangle. What expressions represent the dimensions of the rectangle?
a. | 10x + 7 and 10x – 7 | c. | 10x – 7 and 10x
– 7 | b. | 10x + 7 and 10x + 7 | d. | 10 and 10x2 –
49 |
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15.
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What is the least common multiple of 8x3 –
6x2y2 + 4x2y and
2x2?
a. | 2 | c. | 2x3 – 2x2y2 +
2x2y | b. | 2x2 | d. | 8x3 –
6x2y2 +
4x2y |
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16.
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Which pair of integers has a product of –60 and a sum of 4?
a. | 6 and –10 | c. | 6 and 10 | b. | –6 and 10 | d. | –6 and
–10 |
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17.
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Which of the following options is the factored form of x2 +
6x + 8?
a. | (x + 8)(x + 1) | c. | (x + 3)(x +
2) | b. | (x + 6)(x + 2) | d. | (x + 2)(x +
4) |
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18.
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The area, in metres, of a rectangle is x2 – 10x
– 75. When the expression is factored fully, the factors are the dimensions of the rectangle.
Determine the actual dimensions, in metres, of the rectangle when x = 25.
a. | 10 m by 30 m | c. | 25 m by 35 m | b. | 20 m by 40 m | d. | 30 m by 45 m |
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19.
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Identify the factored form of x2 – 10x +
16.
a. | (x – 5)(x – 5) | c. | (x – 2)(x
– 8) | b. | (x – 4)(x + 4) | d. | (x + 2)(x +
5) |
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20.
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Which of the following expressions cannot be factored?
a. | 3x2 – 13x – 10 | c. | 2x2 + x
– 10 | b. | 2x2 + 9x + 10 | d. | x2 – 3x +
10 |
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Short Answer
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1.
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Apply the distributive property to simplify (5x2 +
10y2)2.
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2.
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Factor 15x2 + 9x + 5x + 3.
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3.
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Factor the trinomial 10x2 – 43x + 28.
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4.
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Factor x2 – 4x + 4.
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5.
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What is special about the expression n2 – 81?
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Problem
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1.
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For each of the following expressions, determine all of the values of k
that allow the trinomial to be factored over the integers. | a) x2 + kx – 19 | b)
2x2 + kx + 15 | | c)
25x2 + kx + 49 | d) (x –
1)2 – k | | |
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2.
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The area of a circle is given by the expression  . a) What is the
diameter of the circle? b) What is its circumference?
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3.
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The first three diagrams in a pattern are shown. 
a) Write an expression for the total number of small squares in the
nth diagram. b) Write an expression for the number of small squares that are shaded
in the nth diagram. c) Write an expression for the number of unshaded small squares
in the nth diagram. d) Write the expression from part c) in factored
form. e) Show that your answers in part c) and part d) give the same number of unshaded
small squares for the 20th diagram.
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4.
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The area of the screen of Javier’s LCD television can be represented by
the binomial 9x2 – 25.
a) Write expressions for the dimensions of
the television screen by fully factoring its area.
b) Determine the actual dimensions of
the television screen if x = 40 cm.
c) What is the perimeter of the screen?
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5.
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Kim owns a square piece of land with a side length of a metres. He
extends his property by purchasing adjacent land so that the length is increased by 10 m and the
width by 12 m. Write an algebraic expression for the area of Kim’s extended property.
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