Factoring Easy and Hard Trinomials MATH 017 Intermediate Algebra S. Rook

2 Overview Section 5.6 in the textbook –Sign analysis –Factoring easy trinomials –Factoring hard trinomials

Sign Analysis

4 Find two numbers that satisfy BOTH of the following conditions: –Multiply to some number x –Add to some number y List all 2-pair factors of x Determine the signs –This task becomes easier if we utilize the rules for products and sums of signed numbers

5 Sign Analysis (Continued) The following chart is helpful:

6 Sign Analysis (Example) Ex 1: Find two numbers that multiply to -24 and add to 5

7 Sign Analysis (Example) Ex 2: Find two numbers that multiply to -40 and add to -13

Factoring Easy Trinomials

9 Has the form x 2 + bx + c –The coefficient in front of the squared term is 1 Goal is to condense the trinomial into a product of two binomials ALWAYS look for a GCF before factoring Look for two numbers whose product is c and sum is b –If two such numbers cannot be found, the polynomial is said to be PRIME (not factorable) Write the binomials

10 Factoring Easy Trinomials (Example) Ex 3: Factor x 2 + x – 20

11 Factoring Easy Trinomials (Example) Ex 4: Factor -x 2 – 14x – 48

12 Factoring Easy Trinomials (Example) Ex 5: Factor 3x 2 – 6x – 9

13 Factoring Easy Trinomials (Example) Ex 6: Factor x 2 + 3x + 9

Factoring Hard Trinomials

15 Factoring Hard Trinomials Has the form ax 2 + bx + c –The coefficient (after factoring out the GCF) in front of the squared term is a number other than 1 Goal is to condense the trinomial into a product of two binomials ALWAYS look for a GCF before factoring Look for two numbers whose product is ac and sum is b –If two such numbers cannot be found, the polynomial is said to be PRIME Factor by grouping

16 Factoring Hard Trinomials (Example) Ex 7: Factor 8x 2 – 10x + 3

17 Factoring Hard Trinomials (Example) Ex 8: Factor 30x 2 – 8x – 8

18 Factoring Hard Trinomials (Example) Ex 9: Factor -54x 2 – 15x – 1

19 Summary After studying these slides, you should know how to do the following: –Find two numbers whose product is x and sum is y –Factor easy trinomials –Factor hard trinomials