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Learning about Polynomials

What's a Polynomial?

Polynomials are algebraic expressions involving variables. They often include exponents, but the exponents must be positive. Polynomials are written in terms, with the largest exponent terms listed first, and the lowest - or terms without exponents - last. Terms are the parts of polynomials - for instance, in the expression 6x^2 + 3y + 1, there are three terms. The first term is 6x^2, the second is 3y and the last is 1.

Polynomial Expressions

Several types of polynomial expressions exist. Sometimes you need to add; other times you need to subtract, to multiply, simplify, factor or 'complete the square.' With polynomial addition, subtraction and multiplication, you should first simplify the expression to its most basic form. From there, you can complete the arithmetic more easily. Sometimes you can evaluate a polynomial expression down to a single polynomial term, meaning you don't have to do any arithmetic.

How to Factor

To factor is to re-write an expression as a sum by extracting its parts. For example, you can factor the number 16 into 8 x 2. Because 16 is a multiple of both 8 and 2, both of those numbers are factors of 16. When you're dealing with polynomials, you need to re-write the given expression (for example, 4y -16) by deciding what number is divisible by both the numbers, and then creating a parenthetical expression to describe it. For instance, with 4y -16, you first want to divide both 4 and 16 by 4, and then re-write the expression as 4(y - 4).

Simplifying Polynomial Expressions

Simplifying an expression means breaking it down into its clearest, most basic form. This can be accomplished by taking a close look at the entire polynomial expression and determining what arithmetic can be performed to make the expression shorter. For example, if you have 3(x + 5), you can break that into 3x + 3 x 5, which can be further reduced to 3x + 15. Now all you have to do is solve for x, and the equation will be complete.