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 7, Lesson 6, page 328 (DAY 2)
Finding an Equation of a Line
There are 2 ways that we can find an equation of a line. However, we need to have at least 2 points `(x,y)` or 1 point `(x,y)` and the slope, `m` provided. If we have those things, we can find the equation by the 2 methods below, you choose the one you like:
A. Using the slope-intercept equation, `y=mx+b`
- (Don’t forget, for this to work, you have to be given the slope, `m`, and at least 1 `(x,y)` point.)
- If you have the slope, `m`, plug it in for `m` above and pick the `(x,y)` that correspond to the point given.
- In the equation then, you have the `y`, `m` and `x` known.
- All you have to do is solve for `b`, the y-intercept.
- Solve for `b`, then plug in the `b` and `m` into the slope-intercept equation.
WARNING: IF you are not given the slope, then you are given 2 points. Given the 2 points, find the slope `m` with the equation `m=(y_2−y_1)/(x_2−x_1)`, then proceed as in step 2 above.
With this method, you have to solve for b, the y-intercept.
B. Using the point-slope equation (which is a derivation of the slope definition), `(y−y_1)=m(x−x_1)`
- (Don’t forget, for this to work, you need the slope and 1 point or at least 2 points from which you can find the slope.)
- (Notice too, that there is NO LONGER a `y_2` and `x_2`, just a `y` and `x`. LEAVE IT THAT WAY!)
- If you have the slope `m`, use it. If you have 2 points, then find the slope – like the WARNING above.
- Choose 1 of the `(x, y)` points to use for `(x_1, y_1)` and plug in the values that you know (`x_1`, `y_1`, and `m`).
- Solve the equation for `y` and remember that you have to distribute on the right side!
With this method you have to you the distribution method on the right. You DO NOT find the `b` or y-intercept.
Either method works, you choose what is most comfortable for YOU!
Here is a link to both methods from purplemath.com.
Two of tonight’s homework problems solved by MrE are here! Just click it!