By Factoring
Word Problems
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### 100

Solve by factoring: (x-2)(x+4)=0
x=2 x=-4

### 100

Solve using quadratic formula: x^2-1=0
x=1 x=-1

### 100

If the dimensions of a rectangle are w=x and l=x-5 and the area is 36cm, what is w and l?
The width of the rectangle is 9cm and the length is 4cm

### 100

x^2-4=0 Graph using a table of values. Show the real roots
x=2 x=-2

Factor 3x^2-45=0
3(x^2-15)=0

### 200

Solve by factoring: x(x-1/2)=0
x=0 x=1/2

### 200

Solve by using quadratic formula: x^2+x-2=0
x=1 x=-2

### 200

The length of a rectangular pool is 5m longer than its width. The area of the pool is 50m^2. What are the dimensions of the pool?
The width of the pool is 5m and the length of the pool is 10m

### 200

Sketch the three possible outcomes when solving a quadratic equation.
1. Two distinct real roots 2. One real root 3. No real roots

### 200

Solve. 5x^2=8x
x=0 x=8/5 (or 1.6)

### 300

Solve by factoring: x^2-6x+8=0
x=4 x=2 (x-4)(x-2)=0

### 300

Solve by using quadratic formula: x^2+6x+5=0
x=-1 x=-5

### 300

The area of the front cover of a daily journal is 273cm^2 and the length is 8cm greater than the width. What are the dimensions of the cover?
The width of the front cover of the journal is 13cm and the length of the front cover is 21cm

### 300

Sketch a graph of 2x^2+x+2, showing the real roots (or x-intercepts) You may use any method you want
There are no real roots. The graph does not intersect the x-axis

### 300

Solve. Round answers to the nearest hundredths 0.1=-2.2x^2-2.4x
x=-1.05 x=-0.04

### 400

Solve by factoring: y^2-3y-10=0
y=5 y=-2 (y-5)(y+2)=0

### 400

Solve by using quadratic formula: x^2+5x+2=0
x=(-5+root(17))/2 x=(-5-root(17))/2

### 400

A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the lawn and the flower bed is 165m^2. What is the width of the flower bed?
The width of the flower bed is 3.5m

### 400

x^2+x-6=0 Sketch the graph, showing the real roots You may use any method you want
x=2 x=-3

### 400

Solve. (x^2-1)/5=7
x=6 x=-6

### 500

Solve by factoring: 2x^2+11x+5=0
x= -5 x= -1/2 (x+5)(2x+1)=0

### 500

-2.2x^2-2.4x=0.1 *round to the nearest hundreth
x=-1.05 x=-0.04

### 500

Adding 19 to the square of the number of provinces in South Africa gives the square of the number of provinces in Canada. How many provinces are there in South Africa?
There are 9 provinces in South Africa *there are 10 provinces in Canada

### 500

2x^2-x-3=0 Sketch the graph, showing the real roots You may use any method you want
x=1.5 x=-1

### 500

Solve. Round to the nearest hundredth. (2x^2)/2+(x)/3=1
x=0.85 x=-1.18