1. 5-4 Factoring Quadratic Expressions Hubarth Algebra II

2. Find the GCF of 2x 4 + 10x 2 – 6x. List the prime factors of each term. Identify the factors common to all terms. 2x 4 = 2 x x x x 10x 2 = 2 5 x x 6x = 2 3 x The GCF is 2x. Ex 1 Finding the Common Factor

3. Factor 4x 3 – 8x 2 + 12x. Step 1: Find the GCF. 4x 3 = 2 2 x x x 8x 2 = 2 2 2 x x 12x = 2 2 3 x Step 2: Factor out the GCF. 4x 3 – 8x 2 + 12x = 4x(x 2 ) + 4x(–2x) + 4x(3) = 4x(x 2 – 2x + 3) The common factor is 2 2 x, or 4x. Ex 2 Factoring Out a Monomial

4. Rules for Factoring a trinomial when the leading term, a = 1. If the c value is positive, you will find the factors of c that add to give you the b value. If the c value is negative, you will find the factors of c that subtract to give you the b value If the c is positive and the b is positive, then both factors will be positive. If the c is positive and the b is negative, then both factors will be negative If the c is negative, then one factor will be negative and one will be positive. If the b is positive, then the larger of the two factors will be positive. If the b is negative, then the larger of the two factors will be negative

5. Ex 3 Factoring 27 127 3 9 (m – 3)(m + 9) 18 118 2 9 3 6 (p – 6)(p + 3)

6. First, multiply the first and last terms. 2 x 2 = 4. 2nd, what are the factors of 4 that add to 5. Note: the sign of the last number tells you to add or subtract to get the middle number. 4 14 2 the factors are 4 and 1 Third, remove the 5y from the original problem and replace with the factors but now include the variable. 4y and y Fourth, you will group the first two terms and the last two. Fifth, now factor out the common monomial in each group. If there is no common monomial it will be 1.

7. Sixth, you will now bring the common monomial factors together and the values in parenthesis become one. These are your two binomial factors and your solution.

8. Ex 1 Factor 1. 6 x 7 = 42 2. Find the factors of 42 that add to 23 42 142 221 314 6 7 2 x 21=42 2 + 21 = 23

9. Ex 2 Factoring 1. 7 x 8 = 56 2. Because the last term is negative you subtract to get the middle value. 56 156 228 414 7 8 2 x 28 =56 2 – 28 = -26 5. 7x(x – 4) +2(x – 4) 6. (7x + 2)(x – 4)

10. Ex 3 Factoring Out a Common Monomial First What is the GCF for each term? 5 is the GCF for 20, 80 and 35 4 x 7 = 28 28 128 214 4 7 2 x 14 = 28 2 + 14 =16 2x(2x + 7)+1(2x + 7) (2x + 1)(2x + 7) Now, place the factors with the monomial factor 5(2x + 1)(2x + 7)

11. To recognize perfect square the first and last terms must be perfect squares. The middle term will be two times the product of the first and last terms square root.

12. Ex 2 Factoring Perfect Squares

13. Both terms need to be perfect squares. The factors are the square roots of each term

14. Practice (3n – 1)(2n – 7) 2(2y + 1)(y + 3)