Algebra: Chapter 5, Lesson 5, page 221
Polynomials
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`
Click here (there are 2 pages) for some examples.
Two of tonight’s homework problems solved by MrE are here! Just click it!
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Algebra 1a: Chapter 4, Lesson 4, page 183.
Using the Properties Together
Inequalities of 2 steps
We do the same, again, as equalities and solve by:
- Distributing when required
- Combining like terms
- Adding or subtracting terms to isolate variables and numbers (constants)
- Multiplying or dividing to finish solving for the variable, remembering to reverse the sign of the inequality IF we multiply or divide by a NEGATIVE NUMBER.
For example:
`7x + 4 ≤ 4x + 16`
subtract `4x` from both sides, that looks like
`7x – 4x + 4 ≤ 4x – 4x + 16`
now combine like terms on the left and the right sides
`3x + 4 ≤ 16`
subtract 4 from each side
`3x + 4 – 4 ≤ 16 – 4`
combine like terms again on both sides, so that
`3x ≤ 12`
and finally divide both sides by 3
`(3x)/3 ≤ 12/3`, so that finally
`x ≤ 4`
Go slow and show all the steps! Here are some more examples from purplemath.com
Two of tonight’s homework problems for Lesson 4 solved by MrE are here! Just click it!