Algebra 1: Factoring Polynomials

Algebra 1: Factoring Polynomials
Name: _______________________________________ Topic F9: Applications of Quadratic Equations | VERSION A 1.
The product of two consecutive even integers is 48. Find the two integers. 5.
The length of a rectangle is 4 inches more than the width. The area is 12 square inches. Find the dimensions. 2.
The product of two consecutive odd integers is 1 less than 6 times their sum. Find the two integers. 6.
The height of a triangle is 2 times the base. The area is 9 square inches. Find the base. 3.
The sum of two integers is 15. Their product is 50. Find the numbers. 7.
The hypotenuse of a right triangle is 10 inches. The lengths of the two legs are given by two consecutive even integers. Find the length of the two legs. 4.
One number is 1 more than 3 times another. Their product is 30. Find the numbers. 8.
A company that manufactures hair ribbons knows that the number of ribbons it can sell each week, 𝑥, is related to the price 𝑝 per ribbon by the equation 𝑥 = 500 − 100𝑝. At what price should the company sell the ribbons if it wants the weekly revenue to be $600? (Remember: The equation for revenue is 𝑅 = 𝑥𝑝.) www.varsitylearning.com 1 Name: _______________________________________ Algebra 1: Factoring Polynomials
Topic F9: Applications of Quadratic Equations | VERSION A 9.
The shorter leg of a right triangle is 5 meters. The hypotenuse is 1 meter longer than the longer leg. Find the length of the longer leg. 10. A company can manufacture 𝑥 hundred items for a total cost of 𝐶 = 400 + 1500𝑥 − 100𝑥 ! . Find 𝑥 if the total cost is $5,800. 11. A 13-‐foot ladder is placed so that it reaches to a point on the wall that is 2 feet higher than twice the distance from the base of the wall to the base of the ladder. 𝑎. How far from the wall is the base of the ladder? 𝑏. How high does the ladder reach? 12. I have a piece of cardboard that is twice as long as it is wide. If I cut a 2-‐inch by 2-‐inch square from each corner and fold up the resulting flaps, I get a box with a volume of 32 cubic inches. What are the dimensions of the cardboard? 13. A gun fires a bullet almost straight up from the edge of a 80-‐foot cliff. If the bullet leaves the gun with a speed of 316 feet per second, its height at time 𝑡 is given by ℎ 𝑡 = −16𝑡 ! + 316𝑡 + 80, measured from the ground below the cliff. When will the bullet land on the ground below the cliff? (Hint: What is its height when it lands? Remember that we are measuring from the ground below, not from the cliff.) 14. If a rocket is fired vertically into the air with a speed of 240 feet per second, its height at time 𝑡 seconds is given by ℎ(𝑡) = −16𝑡 ! + 240𝑡. At what time(s) will the rocket be the following number of feet above the ground? a.
The rocket will 800 feet high after ___________ and __________________ seconds. b.
The rocket will 896 feet high after ___________ and __________________ seconds. c.
How long will the rocket be in the air? (Hint: What time is it when it hits the ground?) www.varsitylearning.com 2 Algebra 1: Factoring Polynomials
Name: _______________________________________ Topic F9: Applications of Quadratic Equations | VERSION A 1.
The product of two consecutive even integers is 48. Find the two integers. 6 and 8 or −8 and −6 5.
The length of a rectangle is 4 inches more than the width. The area is 12 square inches. Find the dimensions. Length: 6 in., width: 2 in. 2.
The product of two consecutive odd integers is 1 less than 6 times their sum. Find the two integers. 11 and 13 or −1 and 1 6.
The height of a triangle is 2 times the base. The area is 9 square inches. Find the base. 3 in. 3.
The sum of two integers is 15. Their product is 50. Find the numbers. 10 and 5 7.
The hypotenuse of a right triangle is 10 inches. The lengths of the two legs are given by two consecutive even integers. Find the length of the two legs. 6 in. and 8 in. 4.
One number is 1 more than 3 times another. Their product is 30. Find the numbers. 8.
A company that manufactures hair ribbons knows that the number of ribbons it can sell each week, 𝑥, is related to the price 𝑝 per ribbon by the equation 𝑥 = 500 − 100𝑝. At what price should the company sell the ribbons if it wants the weekly revenue to be $600? (Remember: The equation for revenue is 𝑅 = 𝑥𝑝.) $2 or $3 −
10
and −9 or 3 and 10 3
www.varsitylearning.com 3 Name: _______________________________________ Algebra 1: Factoring Polynomials
Topic F9: Applications of Quadratic Equations | VERSION A 9.
The shorter leg of a right triangle is 5 meters. The hypotenuse is 1 meter longer than the longer leg. Find the length of the longer leg. 12 m 10. A company can manufacture 𝑥 hundred items for a total cost of 𝐶 = 400 + 1500𝑥 − 100𝑥 ! . Find 𝑥 if the total cost is $5,800. 𝑥 = 6, 9 11. A 13-‐foot ladder is placed so that it reaches to a point on the wall that is 2 feet higher than twice the distance from the base of the wall to the base of the ladder. 𝑎. How far from the wall is the base of the ladder? 5 feet 𝑏. How high does the ladder reach? 12 feet 12. I have a piece of cardboard that is twice as long as it is wide. If I cut a 2-‐inch by 2-‐inch square from each corner and fold up the resulting flaps, I get a box with a volume of 32 cubic inches. What are the dimensions of the cardboard? 12 in. by 6 in 13. A gun fires a bullet almost straight up from the edge of a 80-‐foot cliff. If the bullet leaves the gun with a speed of 316 feet per second, its height at time 𝑡 is given by ℎ 𝑡 = −16𝑡 ! + 316𝑡 + 80, measured from the ground below the cliff. When will the bullet land on the ground below the cliff? (Hint: What is its height when it lands? Remember that we are measuring from the ground below, not from the cliff.) 20 seconds 14. If a rocket is fired vertically into the air with a speed of 240 feet per second, its height at time 𝑡 seconds is given by ℎ(𝑡) = −16𝑡 ! + 240𝑡. At what time(s) will the rocket be the following number of feet above the ground? a.
The rocket will 800 feet high after 5 and 10 seconds. b.
The rocket will 896 feet high after 7 and 8 seconds. c.
How long will the rocket be in the air? (Hint: What time is it when it hits the ground?) 15 seconds www.varsitylearning.com 4

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