How do you do Polynomials
http://mathworld.wolfram.com/Polynomial.html
To perform operations with polynomials, such as addition, subtraction, multiplication, division, and factoring, you can follow these general steps:
1. Understand Polynomials: Polynomials are algebraic expressions with variables raised to non-negative integer exponents. They consist of coefficients, variables, and exponents. For example, "3x^2 - 4x + 2" is a polynomial.
2. Addition and Subtraction: To add or subtract polynomials, line up the like terms (terms with the same variable and exponent) and combine their coefficients. If you encounter terms without a variable, treat them as having a variable with an exponent of 0. For example, to add "3x^2 - 4x + 2" and "2x^2 + 5x - 3", combine the coefficients of like terms: (3 + 2)x^2 + (-4 + 5)x + (2 - 3) = 5x^2 + x - 1.
3. Multiplication: To multiply polynomials, use the distributive property. Multiply each term of one polynomial by each term of the other polynomial, and then combine like terms. For example, to multiply "2x + 3" and "x - 5", multiply each term: (2x)(x) + (2x)(-5) + (3)(x) + (3)(-5) = 2x^2 - 10x + 3x - 15 = 2x^2 - 7x - 15.
4. Division: Polynomial division can be more complex, and it involves long division or synthetic division. Long division is similar to dividing numbers, where you divide the terms, factor by factor, and process each step until you reach the end. Synthetic division is a quicker method but only works for dividing by binomials of the form (x - a). It involves dividing coefficients and bringing down terms. Both methods require knowledge of division rules and factoring.
5. Factoring: Factoring polynomials involves finding their factors, which means breaking down the polynomial into its irreducible factors. This can help simplify or solve equations. There are various factoring techniques, such as factoring out common factors, using difference of squares, using the sum and difference of cubes, and factoring by grouping. Each technique has specific rules and patterns that you can study and apply.
Remember, practice is essential to master polynomial operations. It allows you to recognize patterns and understand the underlying concepts better. Additionally, utilizing algebraic tools or computer software specifically designed for polynomial calculations can be helpful.