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.