Algebra: Chapter 6, Lesson 1, page 262.
Factoring Polynomials
Divisibility Rules
A number is divisible by the numbers below if the following rules hold:
- 2, if the last digit is an even number
- 3, if the sum of the digits is divisible by 3
- 4, if the number formed by the last 2 digits is divisible by 4
- 5, if the number ends in 0 or 5
- 7, the Nike Rule “just do it”, the long division that is
- 9, if the sum of the digits is divisible by 9, similar to the 3 rule above
- 10, if the last digit is 0.
Factoring is the reverse of multiplying. To factor an expression mean to write an equivalent expression that is the product of 2 or more expressions.
To factor a monomial, we find 2 monomials whose product is that monomial. For example `20x^2` has as factors `(4x)(5x)` or `(2x)(10x)` or `(x)(20x)`.
Remember, to multiply a monomial and a polynomial, we use the distributive property to multiply each term of the polynomial by the monomial.
To FACTOR, we do the reverse and FACTOR OUT a common factor. We use the factor COMMON to EACH TERM with the greatest possible coefficient and the variable to the GREATEST POWER.
For example, `16a^2b^2 + 20a^2`
We can re-write it as
`4*4*a^2b^2 + 4*5*a^2`.
The terms that are common are `4a^2` because they are in both terms. So … we can re-write it again (taking out the `4a^2` and putting it on the outside of the parenthesis as
`4a^2(4b^2 + 5)` and that is our FACTORED ANSWER!
Factoring is also described here.
Two of tonight’s homework problems solved by MrE are here! Just click it!
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Algebra 1a: Chapter 8, Lesson 3, page 367.
Addition and Subtraction for 2 linear equations.
You can add 2 (or subtract) linear equations together so that one of the variables cancels out. An example would be:
`3x – y = 9` and `2x + y = 6`
If we line them up, one under the other, we have:
`3x – y = 9`
`2x + y = 6`
Adding them together, we see that the sum looks like `3x + 2x – y + y = 9 + 6`
or
`5x = 15`
and solving for `x` makes it `x = 3`. If `x = 3`, then we can plug it into EITHER original equation, I’ll use the second one and we can solve for `y`.
So… `2x + y = 6`
becomes `2*3 + y = 6` or `6 + y = 6` or `y = 0`. The ordered pair solution is then `(3, 0)`!
We may sometimes have to scale (multiply) ONE OR BOTH of the equations to make one of the variables disappear. Here is a link that can help!
Two of tonight’s homework problems solved by MrE are here! Just click it!