Feb28
- 1. Today: Factoring Unit Test Schedule Warm-Up 2 Factoring Trinomials (x + bx + c) Class Work
- 2. Factoring Test Schedule 1. Monday, March 4-- Prime Factorization, GCF, Factoring using GCF 2. Friday, March 8-- Factor by grouping, Factoring x2 + bx + c Trinomials 3. Thursday, March 14-- Factoring ax2 + bx + c Trinomials, Solving Equations 4. Factoring Special Products, Factoring Difference of Squares
- 3. Warm Up 1. Find the GCF: -18b4 & 27b2 2. What is the highest degree of the GCF for 80 & 96? 3. How many primes are there in the number 64? Factor Out the GCF 4. Factor: 65ab3 - 45a2b2 5. Factor: 12x + 15xy + 21x3 6. Factor: j2 + 9k8
- 4. Factoring Trinomials ( x2 + bx + c) 1 One of the most common types of factoring in algebra is to express a trinomial as the product of two binomials. We're going to look at trinomials that have a coefficient of 1 for the squared term. To begin, let's FOIL the following binomial: (x + 2)(x + 4) The result is: x2 + 4x + 2x + 8; x2 + 6x + 8 Key Point: Notice how the coefficient of middle term is the sum of the F and the I in the FOIL process, and the last term is the product of the O and the L. Now, let's begin where we finished, with: x2 + 6x + 8. To factor this trinomial, we have to find two numbers whose sum is 6, and whose product is 8. Of course, we know those two numbers are 2, & 4: (x + 2)(x + 4)
- 5. Factoring Trinomials ( x2 + bx + c) Example 1: x2 + 7x + 12 It is helpful to set up a table as shown below: Product Sum We can see that the only two numbers whose sum is 7 and 1(12) 1 + 12 whose product is 12, are 3 and 4 2(6) 2+6 (x + 3)(x + 4); FOIL to check 3(4) 3+4 **Example 2: x2 - 2x - 8 ** Products must include negative factors as well. Summary of Signs: ( + )( + ) = Both numbers are positive ( + )( - )= The larger of the 2 numbers is +, the smaller is negative ( - )( + ) = The larger number is negative, the smaller is negative ( - )( - ) = The larger number is negative, the smaller is positive
- 6. Example 3: x2 - 5x + 6 Example 4: x2 + 10x - 24 Finally: These problems should never be incorrect. All you have to do is FOIL your answer to see if you get the original trinomial. It is easy to check for correctness.
- 7. Class Work: Page 20; 2-21 All Must Include Scratch Paper