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 8, Lesson 6, page 387.
Digit and Coin word problems.
Just remember to write the coin problems with the d (dime), q (quarter), n (nickel) preceeded by the value of the coin remembering that the d, q or n stand for the number of that type of coin. For example, `.05n + .10d = 2.05`. You can then multiply both sides by `100` to clear the decimals.
Remember too, that any 2-digit number can be expressed as `10x + y` where `x` is the digit in the tens place and `y` is the digit in the one (units) place. For example, the number `23` can be written as `10 * 2 + 3`. If we reverse the digits in the original number, the new number can be expressed as `10y + x`. The reverse of `23`, `32` can be written as `10 * 3 + 2`.
Here is a link for some examples of coin problems and here is a link for digit type problems (about 1/2 the way down the page)!
Two of tonight’s homework problems solved by MrE are here! Just click it!