SOLUTION: In solving the equation (x + 1)(x � 2) = 4, Eric stated that the solution would be x + 1 = 4 => x = 3 or (x � 2) = 4 => x = 6 However, at least one of these solutions fails to

Question 387689: In solving the equation (x + 1)(x � 2) = 4, Eric stated that the solution would be
x + 1 = 4 => x = 3
or
(x � 2) = 4 => x = 6
However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning.
Found 2 solutions by robertb, rapaljer:
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
For , x-a = c or x - b = c works only if c = 0, and nowhere else. It is called the zero-factor property. To solve this equation, multiply out the left side and then write in standard form, i.e., with zero on one side.
;
;
(x - 3)(x+2) = 0;
x = 3, -2. These are the solutions to the equation.
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
This is a QUADRATIC EQUATION! The error is that problem was solved by using a PROPERTY OF ZERO that does NOT apply to NON-ZERO numbers.

The correct property states that

if x*y=0, then x=0 or y=0.

It is NOT correct to say that if x*y=4 that x=4 or y=4. NOT TRUE!!

The first step is to multiply out the parentheses, and set it equal to zero.
(x+1)(x-2) =4
x^2-2x+1x -2=4
x^2-x-2-4=0
x^2-x-6=0

This does factor into the product of two binomials:
(x-3)(x+2)=0

There are TWO solutions!

First solution:
x-3=0
x=3

Second solution:
x+2=0
x=-2

You may want to check by subsituting both of these numbers into the original equation. I did so, and they both check!

For additional help with SOLVING QUADRATIC EQUATIONS or FACTORING, please take a look at my own website. To see it click on my tutor name "rapaljer" anywhere in algebra.com. Look for the link to my website there. From my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time", click on "Basic Algebra," and then "Chapter 2," which is my chapter on Polynomials. Look in the sections that involve FACTORING, and for QUADRATIC EQUATIONS, see "Section 2.09".

See also the solutions of many of these exercises in the "MATH IN LIVING COLOR" pages, where the problems are solved in COLOR. My own students and others have been unanimous in telling me that my own explanations are easier to understand than the expensive textbooks that are written for mathematicians and publishers!! MY EXPLANATIONS WERE WRITTEN FOR STUDENTS WHO HAVE A HARD TIME UNDERSTANDING MATH!! And they are all FREE!!

If you need help with FACTORING, then I have a VIDEO from my classes a few years before I retired. To see my video FREE, look on my Homepage for the link "Rapalje Videos in Living Color." Choose Basic Algebra, and look for "Factoring". This one and all the other videos are all FREE!!

I hope you like my website!!! If you do, please recommend it to your family and friends!! At least check out the JOKE PAGE--all safe jokes for the little ears in your family!!

Merry Christmas!!!!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

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