Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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What is the product (x + 9)(x – 5)?
a. | x2 + 9x – 45 | c. | x2 –
45x + 4 | b. | x2 – 45x – 45 | d. | x2 + 4x –
45 |
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2.
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Multiply and simplify (x – 7)2.
a. | x2 – 7x + 49 | c. | x2 +
49 | b. | x2 – 14x + 49 | d. | x2 –
49 |
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3.
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Identify the expression that is equal to (4x – 3)(4x +
4).
a. | A = 16x2 + 4x – 12 | c. | A =
16x2 + 28x – 12 | b. | A = 16x2 –
28x – 12 | d. | A = 16x2 – 4x –
12 |
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4.
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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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5.
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The greatest common factor (GCF) for the set of terms 30x, 45x,
60x2, and 30x2 is
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6.
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What is the factored form of the expression –14x + 14?
a. | 2(7x – 7) | c. | –2(7x – 7) | b. | 2(7x +
7) | d. | –2(7x +
7) |
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7.
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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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8.
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The expression –65x2 – 10x + 10 written in
factored form is
a. | –5(–13x2 + 2x – 2) | c. | –5(–13x2 – 2x + 2) | b. | –5(13x2 + 2x – 2) | d. | –5(13x2 –
2x + 2) |
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9.
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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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10.
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Which of the following values of k makes the trinomial
36x2 + kx + 81 a perfect square?
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11.
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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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12.
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The area, in square metres, of Kenny’s driveway is represented by the
expression 196x2. Kenny shovelled 64 m2 of the driveway before taking a
break. Suppose the remaining area of the driveway is rectangular. What are the dimensions of the
rectangle?
a. | 14x + 8 by 14x – 8 | c. | 8 + 14x by 8 –
14x | b. | 14x – 8 by 14x – 8 | d. | 8 – 14x by 8 –
14x |
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13.
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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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14.
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Which of the following pairs of integers has a product of 33 and a sum of
14?
a. | 11 and –3 | c. | 11 and 3 | b. | –11 and 3 | d. | –11 and
–3 |
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15.
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Which of the following pairs of integers has a product of 63 and a sum of
–16?
a. | 7 and 9 | c. | –7 and –9 | b. | 7 and
–9 | d. | –7 and
9 |
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16.
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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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17.
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Choose the factored form of x2 – 17x + 42.
a. | (x – 1)(x – 42) | c. | (x – 3)(x
– 14) | b. | (x – 2)(x – 21) | d. | (x – 6)(x –
7) |
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18.
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What is the factored form of x2 – 3x –
10?
a. | (x – 10)(x – 1) | c. | (x + 5)(x –
2) | b. | (x – 5)(x + 2) | d. | (x + 10)(x –
1) |
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19.
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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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20.
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Identify the factored form of 2x2 + 13x + 20.
a. | (2x + 10)(x + 2) | c. | (2x + 2)(x +
10) | b. | (2x + 5)(x + 4) | d. | (2x + 1)(x +
20) |
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Short Answer
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1.
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What product does the following diagram represent? 
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2.
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Apply the distributive property to simplify (5x2 +
10y2)2.
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3.
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Factor 15x2 + 9x + 5x + 3.
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4.
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Use algebra tiles to factor 2x2 + 6x.
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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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The volume of a prism is given by the expression 18px3 + 48px2 +
32px. What shape could the prism be and what are its
dimensions?
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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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Greg works as a caretaker at a park. In the fall, he rakes all the leaves in the
rectangular park. The length of the park is (3x + 1) m. The width of the park is (2x +
4) m.
a) Develop an expression that represents the area of the park.
b)
Calculate the actual area that Greg has to rake if x = 5 m.
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4.
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The school parking lot is rectangular. Its area can be represented by the
binomial 18x + 6x2.
a) Identify the greatest common factor (GCF)
of the area and write expressions for the dimensions of the parking lot by fully factoring its area.
b) Determine the actual dimensions of the parking lot if x = 8 m.
c)
Write an algebraic expression for the perimeter of the parking lot.
d) Calculate the
actual perimeter for x = 8 m. Verify your answer using the dimensions you found in part
b).
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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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