Відео

Based off the preceding seven exponent topics, I review a simplified version of the rules (for the sake of memorizing), and then cover 23 problems. This is intended to help one organize and "deploy" the concepts necessary to work with a wide variety of problems involving exponents. Matters are not covered in depth, as this is a review.

I describe the series of considerations one follows in adhering to the order of operations as I work through a number of examples. I then follow the order of operations with six more examples, which allows developing a clearer understanding of how to apply these rules. (I do 6 of the 12 problems on the sheet "Order of Operations #1 (Sheet Used in Video)." The complexity ranges from addition and...

I work through 4 problems to show how to factor a difference of squares. Then I work through 2 more to show that factoring a difference of terms raised to the fourth power may require an additional step of factoring. Factoring a difference of squares allows me to finish describing the "Rules for Factoring," that I have been developing through the previous several videos. The Rules provides a st...

I work through 5 more problems, based on concepts covered in the previous video, "Factor Polynomial by Grouping: Introduction (Without Mixed Practice). I do extend slightly on what was covered, but this is mainly to review and reinforce for the sake of one's understanding and long term memory. In the process, I refer to the Rules for Factoring to show how they can be used as a guide for how to ...

I work through 9 problems to show how to "factor by grouping." In the process, I add to the "Rules for Factoring," that I have been developing in the previous few videos on less complicated factoring problems. The Rules will provide some guidance for approaching the wide variety of factoring problems that students will encounter.

I present factored terms of a trinomial to illustrate the concept of GCF prior to factoring it out. Then I cover three more polynomials in which I factor out the GCF more directly. Next I offer three short "rules" one can follow for factoring in general, prior to covering three more trinomials with GCF as the first step. On the last of those, I factor out a negative coefficient to cause the fir...

After showing that the first and last terms of a trinomial are the result of multiplication, while the middle term is the result of addition or subtraction, I present a dependable way to factor trinomials, or see that they are prime. I cover five factoring problems, one of which is prime, in the first 15 minutes. I then offer a mixed practice with five more problems, where one may pause the vid...

I give two brief examples of numbers (from the sciences) written in both standard and scientific notations. Then I go over three examples of converting from standard to scientific notation, and three examples of converting from scientific to standard notation.

Based on rules for positive exponents (with which you should be familiar), I develop the rule for negative exponents, and the rule for zero exponents; this takes the first 5 minutes. In the rest of the video, I go over about 20 examples of simplifying what you are given when negative and/or zero exponents are involved.

I go over 7 examples to illustrate some things to keep in mind as you divide and simplify. After that I cover an additional 3 problems in a "Mixed Practice." The last 3 are basically a review of the previous concepts, but the answers may look slightly different.

I go over 10 examples to illustrate some things to keep in mind as you multiply and simplify. After that I cover an additional 7 problems in a "Mixed Practice." The last 7 are basically a review of the previous concepts.

I cover 3 problems to illustrate the similarity between combining like terms and adding or subtracting polynomials. Then I go over 11 more problems of increasing complexity, with the last two involving the meaning of "subtract from," which can be confusing.

Applying the exponent rules covered in the previous video, "Exponents (Positive)- Rules," I go through 13 examples. Some problems involve more than one rule to simplify the expression.

I cover the rules for operations with positive exponents, from adding (or subtracting), to multiplying, raising to a power, and finally dividing. I develop the rules based on longer methods, which are easier to understand, and then the "shortcut" rules, which are faster and easier to write.

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