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Polynomials
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Polynomials Examples
Negative Exponents
Negative exponents are basically abbreviations for big ugly fractions. In the same way that it's quicker to write LMAO in place of the longer version, negative exponents will make it much easier to...
Variables as Exponents
Since exponents can be any real number and variables are basically the alien decoys of real numbers, we can write down expressions like 2x. We don't love to do it, but we can. We can evaluate these...
Degrees of a Polynomial
Each term in a polynomial has what is called a degree, or a value based on the exponents attached to its variable. The degree of 9x2 is 2, for example. You may be unfamiliar with a degree of 2 unle...
Degrees of Multivariable Polynomials
When finding the degree of a multivariable polynomial, remember to keep your head above ground. That goes for any ostriches who may be reading this. Ignore the constants and look for the exponents...
Evaluating Polynomials
Evaluating a polynomial is like evaluating any other expression. We substitute the given value(s) for each and every variable. Then we do the necessary plusing and minusing to find an answer. If yo...
Combining Polynomials
Adding PolynomialsTo add polynomials, all we do is combine like terms in the same way as we would with any other expression. Sorry, we know you were probably hoping for something new and wildly d...
Multiplication of a Monomial and a Polynomial
The easiest case of polynomial multiplication is multiplying a monomial and a polynomial. In this case, we "distribute" the monomial to each term in the polynomial. We really do distribute it, thou...
Multiplication of Two Binomials
Multiplying two binomials is still an application of the distributive property. In fact, we can use the distributive property even more than we did in the first example. It's like the stuffing and...
Special Cases of Binomial Multiplication
There are some special cases of binomial multiplication that every algebra student should know. Some are useful because they can save you from doing more work than you absolutely need to. Others ar...
General Multiplication of Polynomials
Alas, there are no quick and easy patterns to use when we're multiplying any two polynomials that don't fit the description of one of our special cases. We only need to apply the distributive prope...
The Greatest Common Factor
Been here and done this, but we'll go through a couple of examples to jog your memory. Sorry, we know how much your memory despises physical exercise.Sample ProblemFactor the polynomial x2...
Recognizing Products
Sometimes we can tell by looking at a polynomial that it's a product of a particular type. Not that we want to put polynomials into a box, but...it does preserve their freshness.Difference of Two S...
Trial and Error
We already know how to factor quadratic polynomials that are the result of multiplying a sum and difference, or the result of squaring a binomial with degree 1. Once in a while, though, quadratic p...
Factoring by Grouping
When we use FOIL to multiply two binomials, we multiply the first, outside, inside, and last terms to get four products: (x + y)(a + b) = ax + bx + ay + by.Sometimes we have no choice but...
In the Real World
Scientific NotationEarthshattering fact: Scientists use math. Some mathematicians even use science. Too bad more of them don't use soap. Ooh, ice burn.We're not only talking about whitehaired men...
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