Algebra Section 8-3 Notes Directions: Use this PowerPoint to fill in the note outline provided for you. When indicated, please stop and complete the problems given as practice. Ask the teacher if you have any questions; they will be able to help you through them.

Essential Questions How do I factor a trinomial in the form of x2 + bx + c How do I solve equations in the form of x2 + bx + c = 0

Terms to Know: FACTOR – to express a polynomial (term) as the product (times) of monomials and polynomials EX: 2x = 2 * x EX: 4x2 = 2 * 2 * x * x TRINOMIAL – the sum of three monomials EX: 2 + x + b EX: x2 + 4x + 20

F O I L Use this rule to check your work when you have factored an equation. F = First O = Outer I = Inner L = Last Factor x2 + bx + c: When two numbers are multiplied, each number is a factor of the product. Similarly, when two binomials are multiplied, each binomial is a factor of the product. To factor certain types of trinomials, you will use the pattern for multiplying two binomials. EXAMPLE: (x + 2)(x + 3) = (x *x) + (x * 3) + (x * 2) + (2 * 3) = x2 + 3x + 2x + 6 = x2 + (3 + 2)x + 6 = x2 + 5x + 6

Example 1 Factor x2 + 6x + 8 1. You need to find two numbers with a sum of 6 and a product of 8. 2. Create a table: Factors of 8 Sum of Factors 1, 8 9 2, 4 6 3. x2 + 6x + 8 = (x + 2)(x + 4) 4. Check using FOIL (x + 2)(x + 4) = x2 + 4x + 2x + 8 = x2 + 6x + 8

Use this page to complete the following problems: (hint: follow steps 1-4 from example 1 – show your work and check your results) a2 + 8a + 15 t2 + 10t + 9

Example 2 (when b is negative and c is positive) Factor x2 – 10x + 16 You need to find two numbers with a sum of -10 and a product of 16. Create a table (both numbers must be negative to have a positive product) Factors of 16 Sum of Factors -1, -16 -17 -2, -8 -10 -4, -4 -8 3. x2 – 10x + 16 = (x – 2)(x – 8) Check using FOIL (x – 2)(x – 8) = x2 – 8x – 2x + 16 = x2 – 10x + 16

Use this page to complete the following problems: (hint: follow steps 1-4 from example 2 – show your work and check your results) m2 – 22m + 21 s2 – 11s + 28

Example 3 A (when b is positive and c is negative) Factor x2 + 2x - 15 You need to find two numbers with a sum of 2 and a product of 15. Create a table (one must be positive and one must be negative to have a negative product) Factors of -15 Sum of Factors 1, -15 -14 -1, 15 14 3, -5 -2 -3, 5 2 3. x2 + 2x - 15 = (x – 3)(x + 5) Check using FOIL (x – 3)(x + 5) = x2 + 5x – 3x + 15 = x2 – 10x + 16

Example 3 B (when b and c are both negative) Factor x2 - 7x - 18 You need to find two numbers with a sum of -7 and a product of -18. Create a table (one must be positive and one must be negative to have a negative product) Factors of -18 Sum of Factors 1, -18 -17 -1, 18 17 2, -9 -7 3. x2 - 7x - 18 = (x + 2)(x - 9) Check using FOIL (x + 2)(x - 9) = x2 - 9x + 2x - 18 = x2 – 7x - 18

Use this page to complete the following problems: (hint: follow steps 1-4 from example 3A – show your work and check your results) h2 + 3h - 40 r2 – 2r - 24

Practice Problems: Complete each problem assigned and show your work. Please remember to check your work using FOIL (you will not always have to do this but need to for full credit on these problems until you get better at completing this type of problem) p. 437 #1-6 p. 438 #12-22 odd only