Factoring Word Problems

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Show your work for each problem.

1.
A rectangular field has length meters and width meters. Which expression represents its area?
1. a)
2. b)
3. c)
4. d)
2.
If represents the first of two consecutive integers, what represents their product?
1. a)
2. b)
3. c)
4. d)
3.
A square has side length cm. If the area is 49 square cm, what is ?
4.
The product of two consecutive positive integers is 30. What is the smaller integer?
5.
A ball's height is given by . Which factored form helps find when it hits the ground?
1. a)
2. b)
3. c)
4. d)
6.
A rectangular pool has length 4 meters more than its width. The area is 45 square meters. Find the dimensions.
7.
One number is 3 less than another. Their product is 54. What is the larger number?
8.
A rocket's height is meters after seconds. When does it return to the ground?
9.
Which equation represents: 'The product of two consecutive even integers is 168'?
1. a)
2. b)
3. c)
4. d)
10.
A rectangular garden is twice as long as it is wide. If the area is 72 square meters, what is the width?
11.
A rectangular photo is 6 cm by 8 cm. It has a frame with a uniform border. If the total area is 120 square cm, find the border width.
12.
The sum of a number and its square is 72. Find the positive number.
13.
A ball is thrown upward with height . At what time is the ball at height 32?
1. a) and seconds
2. b) seconds
3. c) seconds
4. d) seconds
14.
The product of two consecutive odd integers is 143. Find the integers.
15.
A rectangular courtyard is 5 meters longer than it is wide. A 2-meter wide walkway surrounds it. If the total area (courtyard + walkway) is 204 square meters, what is the width of the courtyard?