1. a)Factoring by Decomposition Factoring Polynomials: Type 2: Quadratic Trinomials with a Leading coefficient = 1 1.Multiply a and c 2.Look for two numbers that multiply to that product and add to b 3.Break down the middle term into two terms using those two numbers 4.Find the common factor for the first pair and factor it out & then find the common factor for the second pair and factor it out. 5.From the two new terms, place the common factor in one bracket and the factored out factors in the other bracket. The 2 nos. are -20 & 1

2. a)Factoring by Temporary Factors Factoring Polynomials: Type 2: Quadratic Trinomials with a Leading coefficient = 1 The 2 nos. are -20 & 1 1. Multiply a and c 2. Look for two numbers that multiply to that product and add to b 3.Use those numbers as temporary factors. 4.Divide each of the number terms by a and reduce. 5.Multiply one bracket by its denominator

3. a)Factoring using the Windowpane Method Factoring Polynomials: Type 2: Quadratic Trinomials with a Leading coefficient = 1 The 2 nos. are -20 & 1 1. Multiply a and c Look for two numbers that multiply to that product and add to b 2. Draw a Windowpane with four panes. Put the first term in the top left pane and the third term in the bottom right pane. 3. Use the two numbers for two x-terms that you put in the other two panes. 4.Take the common factor out of each row using the sign of the first pane. Take the common factor out of each column using the sign of the top pane. These are your factors.

4. Factoring Special Cases: Type 3: Factoring Perfect Square Trinomials 1.First determine if the first and third terms are perfect squares. Identify their square roots. 2. Determine if the middle term is twice the product of those square roots. If so, then this Trinomial is a Perfect Square Trinomial! 3. Set up two brackets putting the square roots in as the first and second term for each binomial. Perfect Squares And

5. Factoring Special Cases: Type 4: Factoring A Difference of Squares 1.First determine if the two terms are perfect squares. Identify their square roots. 2.Set up two brackets, one with an addition sign and the other with a subtraction sign. They are different, get it? 3.Then insert the square roots in as the first and second term for each binomial. Perfect Squares? A Difference?

6. Factoring Polynomials: Type 5: Completing the Square when the leading coefficient of x 2 = 1 1.Move the constant to the other side. 2.Complete the Square by dividing “b” by 2 and then squaring it. Add this term to both sides. 3.Simplify 4.Express the Perfect Square Trinomial as a Square of a Binomial. 5.Square Root both sides. 6.Move the constant to the other side. This gives us two roots.

7. Factoring Polynomials: Type 5: Completing the Square when the leading coefficient of x 2 = 1 1.Move the constant to the other side. 2.Complete the Square by dividing “b” by 2 and then squaring it. Add this term to both sides. 3.Simplify 4.Express the Perfect Square Trinomial as a Square of a Binomial. 5.Square Root both sides. 6.Move the constant to the other side. This gives us two roots. What if “B’ is an odd number?

8. Factoring Polynomials: Type 5: Completing the Square when the leading coefficient of x 2 = 1 1.Move the constant to the other side. 2.Factor “a” out of the left side 3.Complete the Square by dividing “b” by 2 and then squaring it. Add this term to both sides. 4.Simplify 5.Express the Perfect Square Trinomial as a Square of a Binomial. Divide both sides by “a”. 6.Square Root both sides. 7.Move the constant to the other side. This gives us two roots. What if “a’ is not equal to one?

9. Factoring Polynomials: Type 5: Completing the Square when the leading coefficient of x 2 = 1 1.Move the constant to the other side. 2.Factor “a” out of the left side 3.Complete the Square by dividing “b” by 2 and then squaring it. Add this term to both sides. 4.Simplify 5.Express the Perfect Square Trinomial as a Square of a Binomial. Divide both sides by “a”. 6.Square Root both sides. 7.Move the constant to the other side. This gives us two roots. What if “a’ is not equal to one?