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08 - Learn Synthetic Division of Polynomials - Part 1

By Math and Science

Quality Math And Science Videos that feature step-by-step example problems!

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Synthetic Division | MathHelp.com

In this example, it’s tempting to divide x squared + 5x – 6 by x + 1 by first factoring x squared + 5x – 6. The factors of -6 that add to positive 5 are +6 and -1, so we have x + 6 times x – 1 over x + 1. Notice, however, that nothing cancels. In this situation, we need a different method of dividing the polynomials, so we use long division. In other words, we rewrite x squared + 5x – 6 divided by x + 1 as x + 1 divided into x squared + 5x – 6. Now, our first step in the long division is to determine how many times x goes into x squared. Since x goes into x squared x times, we write an x above the x squared, just like we do with regular long division. Next, we multiply the x times the x + 1 in the divisor to get x squared + x, and we write the x squared + x underneath the x squared + 5x. Next, we subtract x squared + x from x squared + 5x. And watch out for this step: it’s an area where most of the common mistakes in these types of problems are made. Instead of subtracting, I would change the sign of each term in x squared + x, so we have negative x squared + negative x, then add the columns. So we have x squared + negative x squared, which cancels out, and positive 5x + negative x, which is positive 4x. Next, we bring down the -6, in regular long division. Now, we need to determine how many times x goes into 4x. Since x goes into 4x 4 times, we write a positive 4 in our answer. Next, we multiply positive 4 times x + 1 to get 4x + 4, and we write the 4x + 4 underneath the 4x – 6. Next, we subtract 4x + 4 from 4x – 6. In other words, we change the signs on 4x + 4 to -4x + -4, and we add. 4x + -4x cancels out, and -6 + -4 is -10. And since there are no other numbers to bring down, we have a remainder of -10. Finally, remember from the previous example that we add the remainder over the divisor to the quotient. In other words, we add -10 over x + 1 to x + 4, and we have x + 4 + -10 over x + 1. So x squared + 5x – 6 divided by x + 1 simplifies to x + 4 + -10 over x + 1.

Math Antics - Percents Missing Total

By mathantics

Learn multiplication tables in a structured manner (grade 3 math) - very effective!

By Math Mammoth

This method (I call it a structured drill) allows children to learn the multiplication tables in grade 3 or 4 faster and much more effectively than random drilling!

My book Math Mammoth Multiplication 1 at http://www.mathmammoth.com/multiplica... uses this method also. The book covers both the concept of multiplication and the practice of all the tables. It is available both as an instant download and as printed copy.

See a free example lesson from the book:
http://www.mathmammoth.com/preview/Mu...

In the video, I use the table of 3 as an example and go through this three-step method.

In the first step, children memorize the skip-counting list. For the table of 3 this is: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36. They also practice saying it backwards, from 36 to 3.

In the second step, we work with the table itself, but it is written in order so the child can see its structure. The " randomness " comes from me (the teacher) pointing to various problems in a random order. I also like to point out certain benchmark facts to students: 10 x 3 is 30 and 5 x 3 = 15 are such facts because they're in the 10s table and in the 5s table, which the children probably have learned first.

We also practice the tables " backwards " where the " answers " are written and the student tells how many times 3 they are. For example, I point to ___ x 3 = 24, and the child is supposed to say " 8 " . This type of practice makes children learn basic division facts at the same time without realizing it! This really helps third grade students because division is also a topic for third grade math.

Polynomial Long Division | MathHelp.com

By MathHelp.com

Math Antics - Ratios And Rates

By mathantics

SAT Math Part 19 - Long Division of Polynomials

By The Organic Chemistry Tutor

Math Antics - Types of Fractions

By mathantics

The Distributive Property In Arithmetic

By mathantics

Why can't you divide by zero?

By tecmath

Math Antics - Exponents and Square Roots

By mathantics

2nd Grade Math Compilation

By

2nd Grade math is fun with these learning videos! Each lesson can help students with word problems, math games or help prepare for a test! Great for a review of 2nd grade or for an introduction!