1. 5.4 Factoring Polynomials Alg 2

2. The GCF is 5ab. Answer: Distributive Property Factor Factoring with GCF

3. Answer: Factor

4. Group to find the GCF. Factor the GCF of each binomial. Factor Answer: Distributive Property Factoring by Grouping

5. Answer: Factor

6. Rewrite problem using –5y and 3y in place of –2y and factor by grouping. To find the coefficient of the y terms, you must find two numbers whose product is 3(–5) or –15 and whose sum is –2. The two coefficients must be 3 and –5 since and Substitute – 5 y + 3 y for – 2 y. Factor Factor out the GCF of each Answer: Distributive Property Associative Property Factoring 2 or 3 terms

8. Answer: p 2 – 9 is the difference of two squares. Factor out the GCF. Factor Difference of 2 squares

9. This is the sum of two cubes. Answer: Simplify. Sum of two cubes formula with and Factor Difference of 2 cubes

10. This polynomial could be considered the difference of two squares or the difference of two cubes. The difference of two squares should always be done before the difference of two cubes. Difference of two squares Answer: Sum and difference of two cubes Factor

11. Check Use the table feature of your calculator to compare the original expression and the factored form. The table shows that the original function and the factored form have the same function values.

12. Factor each polynomial. a. b. c. d. Answer:

13. Summary Techniques for Factoring Polynomials For any number of terms, check for : Greatest Common Factor For two terms, check for: Differences of two squares a 2 - b 2 = (a + b)(a - b) Sum of two cubes a 3 + b 3 = (a + b)(a 2 – ab + b 2 ) Difference of two cubes a 3 - b 3 = (a - b)(a 2 + ab + b 2 ) For three terms, check for: Perfect square trinomials a 2 + 2ab + b 2 = (a + b) 2 a 2 - 2ab + b 2 = (a - b) 2 General Trinomials acx 2 + (ad +bc)x + bd = (ax +b)(cx + d) For four terms, check for: Grouping Ax + bx + ay + by = x(a + b) + y(a + b) = (a + b) (x + y)

14. Factor the numerator and the denominator. Divide. Assume a  –5, –2. Answer: Therefore, Simplify Quotient of two Trinomials

15. Simplify Answer: