Algebra: Chapter 6, Lesson 6, page 281.
Factoring by Grouping
Factoring by grouping works for polynomials that are greater than trinomials. Grouping usually works with polynomials that have 4 terms. All that you have to do is group the polynomials into binomials using parentheses. But, remember, that not all 4 term expressions can be factored this way.
Example: `6x^3+9x^2+4x+6` becomes `(6x^3+9x^2)+(4x+6)`.
We can factor out a `3x^2` from the first binomial and a `2` from the second binomial leaving us with `(3x^2)(2x+3)+2(2x+3)` or factoring out the `(2x+3)`, we have`(2x+3)(3x^2+2)`.
Here is a link from purplemath.com. She calls it factoring in “pairs”.
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 1 – 3.
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!