Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Melanie’s bedroom floor has a width equal to 10x – 3 and a
length equal to 10x + 7. What equation represents the area of the floor?
a. | A = 100x2 – 100x – 21 | c. | A =
100x2 + 100x – 21 | b. | A = 100x2 + 40x
– 21 | d. | A =
100x2 – 40x – 21 |
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2.
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Multiply and simplify (4x + 7)2.
a. | 16x2 + 56x + 28 | c. | 16x2 + 28x
+ 49 | b. | 16x2 + 56x + 49 | d. | 16x2 +
49 |
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3.
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The area of a rectangle is given as x2 + 2x – 80.
Which expression represents the length of one side of the rectangle?
a. | x – 80 | c. | x – 8 | b. | x + 80 | d. | x + 8 |
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4.
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The greatest common factor (GCF) for a polynomial can be
a. | a constant | b. | a constant, a variable, or a constant with a
variable | c. | a constant with a variable | d. | a variable |
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5.
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What is the factored form of the expression –30x + 102?
a. | 6(5x – 17) | c. | –6(5x –
17) | b. | 6(5x + 17) | d. | –6(5x + 17) |
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6.
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The expression –12x2 – 60x written in fully
factored form is
a. | –12x(x + 5) | c. | –12(x2 +
5x) | b. | –6x(2x + 10) | d. | –12(x2 –
5x) |
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7.
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What is the expression –99x2 – 18x + 36 in
factored form?
a. | –9(11x2 + 2x – 4) | c. | –9(11x2
– 2x + 4) | b. | –9(–11x2 –
2x + 4) | d. | –9(–11x2 + 2x –
4) |
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8.
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What is the factored form of the expression 5x2 –
45?
a. | 5x2(x – 9) | c. | 5x(x2
– 9) | b. | 5x(x – 9) | d. | 5(x2 –
9) |
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9.
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The area of a rectangular school gym floor is represented by the equation
A = 120x2 + 1800x. When the expression is factored fully, the factors
are the dimensions of the floor. The dimensions of the floor are
a. | 12x by x + 15 | c. | 60x by 2x +
30 | b. | 12x by 10x + 15 | d. | 120x by x +
15 |
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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 value of k makes the trinomial 16x2 + 40x
+ k a perfect square?
a. |  | c. | 25 | b. | 100 | d. | 12.5 |
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12.
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Suppose the area of a rectangle is represented by the expression
25x2 – 4. When the expression is fully factored, the factors represent the
dimensions of the rectangle. What expressions represent the dimensions of the rectangle?
a. | 5x + 2 and 5x – 2 | c. | 5x – 2 and 5x
– 2 | b. | 5x + 2 and 5x + 2 | d. | 5 and 5x2 –
4 |
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13.
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The area, in square metres, of Kenny’s driveway is represented by the
expression 196x2. Kenny shovelled 49 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 + 7 by 14x – 7 | c. | 7 + 14x by 7 –
14x | b. | 14x – 7 by 14x – 7 | d. | 7 – 14x by 7 –
14x |
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14.
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Which expression is equivalent to 16m2 – 64m +
64?
a. | (4m + 8)2 | c. | (4m –
4096)2 | b. | (4m –
8m)2 | d. | (4m – 8)2 |
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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 12 and a sum of –8?
a. | 2 and 6 | c. | 2 and –6 | b. | –2 and –6 | d. | –2 and 6 |
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17.
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Which of the following pairs of integers has a product of –45 and a sum of
4?
a. | –9 and 5 | c. | 9 and –5 | b. | –9 and –5 | d. | 9 and 5 |
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18.
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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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19.
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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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20.
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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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Short Answer
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1.
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What is the simplified form of the product (4x2 + 6x +
5)2?
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2.
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Determine the greatest common factor of the numbers 12, 54, and 72.
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3.
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Factor 16x(a + b + c) + 7y(a +
b + c) + 8w(a + b + c).
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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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Factor 100x2 + 100x + 25.
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Problem
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1.
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Brittany is checking whether the pool she wants to buy will fit in her backyard.
The pool with the patio measures 4 m by 5 m. Refer to the diagram below. a) Write an
algebraic expression, in factored form, for the shaded area. b) When Brittany measures her
yard, she notices that x = 3, but she needs 20 m 2 for her dog to run. Will the pool
fit in her yard? 
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2.
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Determine all of the positive values of k for which x2
+ 12x + k is factorable over the integers.
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3.
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The figure below consists of a smaller square inside a larger one. The
difference in their areas (the shaded part) is 17 cm 2. The sum of the perimeters of the
two squares is 68 cm. How long are the sides of the larger square? 
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4.
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A rectangular prism has a width of x cm. Its length is 3 cm more than its
width, and its height is 4 cm more than its length. Write an algebraic expression, in simplified
form, for the volume of the prism.
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5.
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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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