# Download PDF by Gregory P. Bullock Ph.D.: Algebra in Words: A Guide of Hints, Strategies and Simple

By Gregory P. Bullock Ph.D.

ISBN-10: 1499701551

ISBN-13: 9781499701555

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Additional info for Algebra in Words: A Guide of Hints, Strategies and Simple Explanations

Example text

Property Crises of Zeros, Ones & Negatives There are many fundamental properties involving various operations with 0, 1 and negative numbers (I will focus mostly on “-1”). Some are easy to remember, however, some are easy to confuse or forget, but they are vital to get right. In textbooks, these are often thrown at you from different directions, at different times, often with vocabulary or definition-like labels. These are properties involving multiplication, division, exponents and roots. For ease and convenience, I’ve summarized the important ones here in this section, leaving out the labels, but showing the property, then explaining it in words, the way you might say it, hear it, or hear it in your head.

Consider the terms: 3x2 and 4x2. They are like and can be multiplied to get 12x4. What is a Factor? A factor is a number or variable that is or can be multiplied by another number or variable. Factors combine via multiplication to make a term (and yes, factors are multiplied to give a product, but this section is meant to help distinguish between factors and terms, as they are often used incorrectly interchageably). But often times, to serve their function, factors are not multiplied together, rather they are factored from larger numbers or terms and shown as unmultiplied, individual factors.

If it is prime, you cannot factor it. This is useful to know when you are factoring numbers (sometimes using a factor tree; see your textbook for more on factor trees); when doing factor trees, your goal is to factor all numbers into prime numbers. This may be used when finding an LCD or in the process of factoring trinomials into binomials. You also use factoring with radicals, but in those cases, you don’t always need to factor to prime numbers. For more on that, see: Manipulating & Simplifying Radicals.