Factorization and the aMAZEing Math Maze

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Wow!  Factorization!!  Like many mysterious math words, it sure sounds impressive, but really isn't.  I will cover factorization in more detail at the end of this page.  First I want to talk with the people who are taking the aMAZEing Math Maze and had some trouble with question #14.

We wanted you to find which one of the trinomials couldn't be factored using integers.  First of all, I think the problem is probably more about vocabulary than mathematics.  Trinomials are expressions or equations with three terms.  All four of the answer choices had three terms, so no much help there.

Integer is a Latin word that means whole.  However whole numbers are all the positive numbers and zero, while integers is all the negative numbers in addition to all the whole numbers.  Factors are the parts of something.

In this question we want to know which of the expressions can be broken into integer parts that can be multiplied together to give you the whole expression.  Each of the terms are quadratics, so we could check them with the quadratic formula, but that seems to be way too much work.  Here's a rule that I am sure you've heard before -

When factoring a quadratic where the coefficient of the squared variable is 1, find two integers that multiply together to give you the third term and add together to give you the coefficient of the middle term.

So, let's look at the first possible answer.  x^2 + 3x - 10  - are there two numbers that multiply together to give us -10 and add together to give us +3?  What about (-2) and (5)?  (-2)(5) = -10 and -2 + 5 = 3.

The second possible answer is x^2 + x - 12 - What about (-3)(4) = -12 and -3 + 4 = 1.

The third possible answer x^2 + 2x -1  - Well, the only two numbers that multiply together to give you -1 are (1) and (-1) which add together to give you 0.  So the answer is C) x^2 + 2x -1.

What the heck, let's do the fourth answer.  x^2 + 2x -3.  (-1) and (3) multiply to give us -3 and add to give +2.

Fun stuff.  Let's see if you can answer a similar question now.

The aMAZEing Math Maze Question 12b

Which one of these trinomials can not be factored using integers?

A) x2 + 4x + 4

B) x2 + x - 20

C) x2 + 4x - 5

D) x2 + 4x + 5

Which of the above could not be factored using integers?

A)  B)  C)  D)

Factorization

Well, a bit more about Factorization.  They define the word pretty well over at Wikipedia.  The example above is from the aMAZEing Math Maze and it describes how to factor a quadratic.  Algebra is all about factorization, in fact it would be a better name for it than Algebra which is an abbreviation of the book title Hidab al-jabr wal-muqubala which, I have heard, wasn't an extremely innovative book.

To learn to factor, study Algebra.  To study Algebra 1 - go to myhsmath.com 

Math is literally everywhere you happen to look.  This ceiling makes it obvious as each of the grid sections is subdivided into another grid of rectangles.

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