Algebra: Chapter 5-5 and 5-6, p 221 and 226 (Thursday)
Polynomials and More
Polynomials is the catch term for monomials put together with + or − signs. Polynomials with just 1 term are called “monomials”, with 2 terms they are called “binomials”, with 3 terms, they are called “trinomials”. Polynomials with more than 3 terms have no particular name.
TERMS are separated by + or − signs and the FACTORS are the things that are multiplied together to get each term. The numeric factor of a term is called a COEFFICIENT and terms with just numbers (no variables) are called CONSTANTS.
The DEGREE (or ORDER) of a term is the sum of the exponents of the variables and the degree of a polynomial is the highest degree of its terms. The term with the highest degree is called the LEADING TERM and the coefficient of the leading term is called the LEADING COEFFICIENT.
We can simplify a polynomial by collecting LIKE TERMS. Like terms MUST have the same variables in the terms AND must have the same exponent values, this part is important.
Examples: `2m^3 − 6m^3 = (2−6)m^3 = −4m^3`
`5x^3 + 6x^3 + 4 = 11x^3 + 4`
We can write polynomials is ascending or descending order. For descending order, the term with the greatest exponent for our variable of interest is first, the term with the next greatest exponent for x is second and ….
Finally, we can evaluate polynomials when we replace the variable by a number and calculate the resulting answer. This is called EVALUATING THE POLYNOMIAL.
Click here for some examples and hints from purplemath.com
Algebra: Chapter 5-3 and 5-4, p 214 and 217 (Wednesday)
Multiplying and Dividing Monomials and Scientific Notation
A monomial is an expression that is either a NUMERAL, an VARIABLE or a PRODUCT of numerals and variables with whole number exponents. If the monomial is a numeral, we call it a CONSTANT.
Using the properties we had from yesterday, we can use the associative and commutative properties to multiply or divide monomials.
For example, `(3x)(4x) = (3*4*x*x) = 12x^2` or
`(x^5)/(x^2) = x^(5-2) = x^3`
Here are some more examples too!
Scientific Notation
We can write numbers as the product of a power of 10 and a number greater than 1 but less than 10 (9.9999…. to be exact). Standard notationis the stuff that we are normally used to.
Examples: `4.58 * 10^4 = 45,800`
`(3.0 * 10^5)(4.1 *10^(-3)) = (3.0*4.1*10^5*10^(-3) = 12.3*10^2 = 1.23*10^3`