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Solving by Factoring
Solving
Word Problems
Word problems
100
Solve x^2-5x+6=0
x=2 x=3
100

Solve x^2-9=0

x=3 x=-3

100

A rectangular garden is 6 meters longer than it is wide. The area of the garden is 16 square meters. Find the length and width of the garden.

The garden is 2 meters wide, and its length is 8 meters.

200
Solve x^2=3x+4
x=-1 x=4
200
Solve x^2-7x=0
x=0 x=7
200

The perimeter of a rectangle is 30 centimeters, and the area is 54 square centimeters. Find the width and length of the rectangle. [Hint: Let w represent the width; then 15 - w represents the length.]

The dimensions of the rectangle are 6 x 9 cm.

300
Solve 3x^2+8=14
x=2/3 x=4
300
Solve 2x^3+4x^2-16x=0
x=-4 x=2
300

The product of two consecutive odd whole numbers is one less than five times their sum. Find the numbers.

The numbers are 2 and 11.

300

The longer leg of a right triangle is one unit shorter than twice the length of the shorter leg. The hypotenuse is one unit longer than twice the length of the shorter leg. Find the lengths of the three sides of the triangle.

The dimensions of the triangle are 8 cm, 15 cm and 17 cm.

400
Solve (x+3)^2=9
x=-6 x=0
400
Solve 4x^2=-12x-5
x=-5/2 x=-1/2
400

The path of a ball is modeled by the equation H=-16t^2+11t+5. How long does it take for the ball to hit the ground? (aka h = 0) and yes this is factorable

t=1 second

400

The sum of the areas of a square and a rectangle is 64 square centimeters. The length of the rectangle is 4 centimeters more than a side of the square, and the width of the rectangle is 2 centimeters more than a side of the square. Find the dimensions of the rectangle and the square.

The side of the square is 4 cm and the dimensions of the rectangle are 8 x 6 cm.

500

Solve 18x^2-39x=15

You will get fractions as your answers

x=-1/3 x=5/2

500

Solve 18x^2-39x=-20

You will get fractions as your answers

x=5/6 x=4/3

500

The length of a rectangular vegetable garden is 4 feet more than its width. After a 2 foot cement border is placed around the garden, the area of garden and border is 320 square feet. Find the original dimensions of the vegetable garden.

The garden is 12 feet by 16 feet.

500

If a triangle's height is 4 inches less than two times its base and has an area of 120 square inches. What is the height of the triangle? 


(area of triangle = 1/2 *b*h)

The height of the triangle is 20 inches.