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Polynomials And Factoring
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Polynomials are the sums of exponents and variables. For example, if you take the expression 6x2 or 9x, the polynomial is the sum of its exponents and variables. The part of the polynomial is called terms. Generally, some terms of polynomials have variables that are raised as whole number exponents. With these whole number exponents, you find no square root variables. They have zero variables of the denominator of every fraction and zero fractional powers. If you take 8x -3 you can understand it is not a polynomial term, as it has negative exponents with its variable. Neither 2/x2 is a term of a polynomial nor sbrt(x) is a term of a polynomial, as the first example has the variable in the denominator while second one has its variable inside a radical. Nevertheless, 6x2 is a polynomial term, as it harmonizes with all the above rules.
You can write a typical polynomials like 4x2 + 3x - 7. Here the term 4x2 is the leading term while the seven is the constant term, as there is no any exponents, or variables. The exponents of the first term is the number 2 and the second has an understood exponent 1 while the 3rd term has no variables, or exponent. Normally, polynomial is written with the largest first. The last one is the plain number.
If you are familiar with multiplying of polynomials, you can understand that polynomial factoring is the opposite of it. Now if you go to the basic of the polynomials and factoring, you can remember that when finding factors, we are looking for prime factors that we have to multiply to get the number. For example we can take 8 = 2* 4, or 15 = 3* 5*. When you have to factor a polynomial, you should look for simpler numbers that you could multiply easily to give the polynomial, which you started factoring with.
The easiest way to factor polynomials is to remove common factors from terms. To do this, you have to find the common factor of all. Now, you have to use the reverse pattern of the distributive law. The simplest example for the distributive law in reverse is ab +ac and write that as a(b+c). Another example is 2x2 + 4x. Here you can see that every term includes the factor 2x. We can factor it like 2x2 + 4x = 2x (x + 2). These are some simplifications of the polynomials and factoring. When you know the basics of polynomials and factors you can easily factor polynomials.