Algebra: Chapter 6, Lesson 7, page 283.
Factoring: A General Strategy
To factor polynomials:
- Always look first for a common factor
- Then look at the number of terms
- 2 terms – determine whether you have a difference of 2 squares
- 3 terms – determine whether the trinomial is a square of a binomial. If not, test the factors of the terms.
- Always factor completely!
Use all the strategies we’ve learned so far to factor a variety of problems. Don’t forget to use:
- Monomial factorization (lesson 6-1)
- The differences of 2 squares (lesson 6-2), `(a^2 – b^2) = (a – b)(a + b)`
- Trinomial squares (lesson 6-3), `a^2 + 2ab + b^2 = (a + b)^2` or with a negative `(-2ab)`
- The BOX METHOD (lesson 6-4 and 6-5) for `x^2 + bx + c` or `ax^2 + bx + c` type of equations
- Factoring by grouping (lesson 6-6) for polynomials with 4 or more terms.
The toughest part is figuring out what technique to use! Go slow and you’ll be OK!
Two of tonight’s homework problems solved by MrE are here! Just click it!
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Algebra 1a: Chapter 7, Lesson 7, page 333.
Fitting Equations to Data
“The mathematical relationship between 2 variables is of interest in many real-world situations. The relationship between 2 variables can often be expressed as a linear equation, which is calleda model of the situation. The model can be use to make estimates or predictions about the quantities represented by the variables.”
In the problems with real-world data, we sometimes have to approximate, by plotting the data on a x-y graph and then drawing (fitting) a line the best way we can through MOST of the data. We can then use 2 of the points on our line to use to develop our linear equation.
We can use either the slope-intercept equation (`y = mx + b`) or the point-slope equation [`y – y_1 = m(x – x_1)`] to develop our linear equation.
Two of tonight’s homework problems solved by MrE are here! Just click it!