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 + 4)(x – 2)?
a. | x2 + 4x – 8 | c. | x2 –
8x + 2 | b. | x2 – 8x – 8 | d. | x2 + 2x –
8 |
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2.
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Multiply and simplify (x + 20)2.
a. | x2 + 20x + 400 | c. | x2 +
400 | b. | x2 + 40x + 400 | d. | x2 –
400 |
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3.
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Identify the expression that is equal to (4x + 3)(6x + 6).
a. | A = 24x2 + 42x + 18 | c. | A = 24x2 +
6x + 18 | b. | A = 24x2 – 6x + 18 | d. | A = 24x2 –
42x + 18 |
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4.
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Multiply and simplify (7x + 3)2.
a. | 49x2 + 42x + 21 | c. | 49x2 + 21x
+ 9 | b. | 49x2 + 42x + 9 | d. | 49x2 +
9 |
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5.
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What expression represents the surface area of a cube with a side length of
(x – 5) units?
a. | 6x2 – 60x + 150 | c. | x3 –
15x2 + 75x – 125 | b. | x2 – 10x +
25 | d. | 6x2 +
150 |
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6.
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The area of a rectangle is given as x2 + 4x + 4. Which
expression represents the length of one side of the rectangle?
a. | x + 4 | c. | x + 2 | b. | x – 4 | d. | x –
2 |
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7.
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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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8.
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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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9.
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The greatest common factor (GCF) for the set of terms 30x, 45x,
60x2, and 30x2 is
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10.
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The expression –2x2 – 10x written in fully
factored form is
a. | –2x(x + 5) | c. | –2(x2 +
5x) | b. | –x(2x + 10) | d. | –2(x2 –
5x) |
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11.
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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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12.
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The expression –78x2 + 12x + 12 written in
factored form is
a. | –6(–13x2 – 2x – 2) | c. | –6(–13x2 + 2x + 2) | b. | –6(13x2 – 2x – 2) | d. | –6(13x2 + 2x +
2) |
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13.
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What is the expression –21x2 – 18x + 12 in
factored form?
a. | –3(7x2 + 6x – 4) | c. | –3(7x2
– 6x + 4) | b. | –3(–7x2 –
6x + 4) | d. | –3(–7x2 + 6x –
4) |
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14.
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What is the factored form of the expression –5x2 +
5?
a. | –5x2(x – ) | c. | –5x(x2 – ) | b. | –5x(x – ) | d. | –5(x2 –
) |
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15.
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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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16.
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Which expression is equivalent to 64m2 + 128m +
64?
a. | (8m – 8)2 | c. | (8m –
4096)2 | b. | (8m +
8m)2 | d. | (8m + 8)2 |
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17.
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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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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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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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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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What is the simplified form of the product (5x2 + 2x +
4)2?
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3.
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Use algebra tiles to factor 2x2 + 6x.
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4.
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Use algebra tiles or a diagram to factor the trinomial x2 +
7x + 6.
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5.
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Factor 3x3 + 9x2 – 3x –
9.
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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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When the McKay family has a reunion, it is a tradition for each family member to
shake hands with each of the other family members. Last year there were a total of 36 handshakes. The
total number of handshakes, H, possible for x people is given by H =  .
How many people were at the McKay family reunion last year?
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3.
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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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4.
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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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5.
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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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