Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Multiply and simplify (3x + 3)2.
a. | 9x2 + 18x + 9 | c. | 9x2 + 9x +
9 | b. | 9x2 + 18x + 9 | d. | 9x2 +
9 |
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2.
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What is the greatest common factor (GCF) for the following set of terms? 12,
4x, 8x2, 16x2
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3.
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What is the factored form of the expression –8x + 20?
a. | 4(2x – 5) | c. | –4(2x – 5) | b. | 4(2x +
5) | d. | –4(2x +
5) |
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4.
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Which of the following expressions is the factored form of 3x(y +
1) + 4z(y + 1)?
a. | (3x + 4z)(y + 1) | c. | (3x + 1)(4z +
y) | b. | (3x + y)(4z + 1) | d. | (3xy + 1)(4z +
1) |
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5.
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What is the expression –50x2 + 30x – 15 in
factored form?
a. | –5(10x2 – 6x + 3) | c. | –5(10x2 +
6x – 3) | b. | –5(–10x2 +
6x – 3) | d. | –5(–10x2 – 6x +
3) |
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6.
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Which of the following values of k makes the trinomial
100x2 + kx + 49 a perfect square?
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7.
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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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8.
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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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9.
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Factor x2 – 324.
a. | (x + 18)(x – 18) | c. | (x + 18)(x +
18) | b. | (x – 18)(x – 18) | d. | cannot be
factored |
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10.
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Which value of k makes the trinomial 4x2 + 8x +
k a perfect square?
a. |  | c. | 4 | b. | 16 | d. | 2 |
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11.
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Which expression is equal to (a – b)2?
a. | a2 – ab + b2 | c. | a2 + ab + b2 | b. | a2
– 2ab + b2 | d. | a2 + 2ab +
b2 |
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12.
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Which expression is equivalent to x2 – 20x +
100?
a. | (x + 10)2 | c. | (x + 10)(x +
10) | b. | (x – 10)2 | d. | (x – 10)(x +
10) |
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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 –1 and a sum of
0?
a. | –1 and –1 | c. | –1 and 1 | b. | 1 and 1 | d. | 1 and –1 |
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15.
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Identify the pair of integers that has a product of 48 and a sum of 14.
a. | –6 and 8 | c. | 6 and –8 | b. | –6 and –8 | d. | 6 and 8 |
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16.
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Which of the following pairs of integers has a product of –99 and a sum of
–2?
a. | 11 and –9 | c. | –11 and 9 | b. | 11 and 9 | d. | –11 and
–9 |
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17.
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What is the factored form of 72 + 27x + x2?
a. | (x + 12)(x + 6) | c. | (x + 3)(x +
24) | b. | (x + 9)(x + 8) | d. | (x + 2)(x +
3) |
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18.
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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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19.
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What is the factored form of 6x2 + 17x + 5?
a. | (6x + 1)(3x + 5) | c. | (3x + 1)(2x +
5) | b. | (3x + 5)(2x + 1) | d. | (2x + 5)(3x +
1) |
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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 is the simplified form of the product (2x2 + 6x +
2)2?
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2.
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Factor 16x(a + b + c) + 7y(a +
b + c) + 8w(a + b + c).
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3.
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Factor the trinomial 10x2 – 43x + 28.
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4.
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What is the factored form of the trinomial 30x2 –
25xy – 30y2?
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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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At a CFL game, foam footballs are launched in a pre-game promotion. The balls
are launched from a height of 1 m above the field. The vertical motion of a ball can be modelled by
the relation h = –5t2 + 30t + 1, where t is time in
seconds, and h is the height in metres. If a fan who is in the stands 26 m above the field
catches a ball when it is on the way down, how long was the ball in the air?
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2.
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The formula  gives the number of diagonals in a polygon with n
sides. Write this formula in factored form and determine the number of diagonals in each of the
following polygons. a) an octagon b) a decagon c) a polygon with 100
sides
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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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Jorge has prepared his science project on a piece of poster board that has an
area represented by the trinomial x2 + 5x – 50.
a)
What are the dimensions of the board?
b) Write an expression for the perimeter of the
board.
c) What is the actual perimeter of the board if x = 90 cm?
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5.
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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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