Algebra Period 3

Using Equations that Factor 6-9

Word Problems

Problem Solving Guidelines

Phase 1: Understanding the problem
Ask yourself:

What am I trying to find?
What data am I given?
Have I ever solved a similar problem?

Phase 2: Develop and carryout a PLAN

Ask yourself:

What strategies might I use to solve the problem?
How can I correctly carry out the strategies I selected?

Phase 3: Find the ANSWER and CHECK

Ask Yourself:

Does the proposed solution check?
What is the answer to the problem?
Does the answer seem reasonable?
Have a stated the answer clearly? ( labeled??)


Practice translating some of these word problems:

The product of one more than a number and one less than the number is 8.
Find the number.

Start with a let statement. It can be as simple as
Let x = the number.

the product... means it will be a multiplication problem
one more than a number x + 1
one less than the number x - 1

so (x +1)(x- 1) = 8

in order to solve you must use FOIL or the box method
but just looking at ( x + 1) (x -1) you know that is the difference of 2 squares... so
x² - 1 = 8 move the eight to the other side setting the equation equal to 0

x² - 9 = 0 and now it is also the difference of two squares or
(x-3)(x+3) = 0

so x - 3 = 0 and x + 3 = 0 so x = + 3 OR x = -3



The square of a number minus twice the number is 48. Find the number

Let x = the number

the square of a number x²
minus twice the number -2x

so x² -2x = 48

again it becones x² -2x - 48 = 0

factor and you get (x -8)(x+6) = 0 Using the principle of Zero products
x = 8 or x = -6