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 greatest common factor of 280 and 360.
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2.
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Determine the greatest common factor of 84, 210, and 336.
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3.
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A developer wants to subdivide a rectangular plot of land measuring 600 m by 750
m into congruent square lots. What is the side length of the largest possible square?
a. | 75 m | b. | 30 m | c. | 150 m | d. | 50 m |
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4.
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What is the side length of the smallest square that could be tiled using a 6-cm
by 15-cm tile? Assume the tiles cannot be cut.
a. | 10 cm | b. | 90 cm | c. | 30 cm | d. | 3
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5.
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Identify the greatest common factor of the terms in the trinomial  .
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6.
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Factor the trinomial  .
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7.
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Factor: 
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8.
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Factor: 
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9.
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Factor: 
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10.
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Expand and simplify: 
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11.
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Factor: 
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12.
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Which set of algebra tiles represents  ?
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13.
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Factor: 
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14.
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Factor: 
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15.
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Expand and simplify: 
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16.
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Factor: 
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17.
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Factor: 
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18.
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Factor: 
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19.
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Identify this polynomial as a perfect square trinomial, a difference of squares,
or neither.  a. | Difference of squares | c. | Neither | b. | Perfect square
trinomial |
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20.
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Determine the area of the shaded region in factored form. 
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Short Answer
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21.
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Determine the least common multiple of 450 and 180.
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22.
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Simplify  , then factor.
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23.
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Expand and simplify: 
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24.
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Factor: 
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25.
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Factor fully: 
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Problem
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26.
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Chris completes one lap of a go-cart track every 40 s. D’Arcy completes
one lap of the same track every 50 s. Suppose Chris and D’Arcy cross the starting line at the
same time. How many seconds will pass before they cross the starting line at the same time again? How
many laps will Chris have completed in that time? How many laps will D’Arcy have completed in
that time?
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27.
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A rectangle is divided into 2 smaller rectangles. The area of the rectangle on
the left is 209 square inches, and the area of the rectangle on the right is 319 square inches.
Determine the greatest possible measure of the side that the two rectangles share. 
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28.
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Jordan wants to cut a rectangular carpet with dimensions 32 cm by 80 cm into
squares of equal size.
a) What is the side length of the largest
possible square Jordan can cut?
b) How many squares can she cut
from carpet?
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29.
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Factor. Check by expanding. 
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30.
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Use decomposition to factor  . Explain your steps.
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