Greatest Common Factor To factor a polynomial whose terms have a common factor: Find the greatest common factor. Divide by the common factor. The common actor is one factor and the quotient is the other factor. When multiplied, the two factors should be equal to the original expression.

Examples of Greatest Common Factor Example 1 Example b The smallest exponent is the greatest common factor. Example 3Example d Example 5

Multiplying the Sum & Difference of Two Terms Let’s use foil first. First Outside Inside Last This is a stupid human trick that makes this easier.

Examples of Multiplying the Sum & Difference of Two Terms Remember the stupid human trick. Example 1Example b That was easy

Factoring the Difference of Two Perfect Squares a2 a2 - b2 b2 is the Difference of Two Perfect Squares because each term is a perfect square and there’s subtraction between them. Factoring Difference of Two Perfect Squares is the reverse of multiplying the sum & difference of two terms.

Examples of Factoring the Difference of Two Perfect Squares Example 1Example b That was easy

Multiplying Binomials Remember to use foil. The binomials each had the same signs and in the resulting trinomial, the middle term has that sign and the 3 rd term is positive. The binomials each had opposite signs and in the resulting trinomial, the middle term has the sign of the larger number and the 3 rd term is negative.

Factoring Trinomials There are a few things to remember when factoring a trinomial. 1)A trinomial factors into 2 binomials. 2) The product of the 2 first terms equals the 1 st term of the trinomial. 3)The product of the 2 second terms equals the 3 rd term of the trinomial. 4)The sum of the 2 second terms equals the 2 nd term of the trinomial. 1)A trinomial factors into 2 binomials. 2) The product of the 2 first terms equals the 1 st term of the trinomial. 3) The product of the 2 second terms equals the 3 rd term of the trinomial. 4) The sum of the 2 second terms equals the 2 nd term of the trinomial.

Examples of Factoring Trinomials 3 rd term is positive so signs are the same. 2nd term is positive so both signs are positive. 3 rd term is positive so signs are the same. 2nd term is negative so both signs are negative. 3 rd term is negative so signs are opposite. 2nd term is positive so the larger number is positive. 3 rd term is negative so signs are opposite. 2nd term is negative so the larger number is negative. That was easy