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## Math 105- Week 4

by: Cassandra Notetaker

25

0

3

# Math 105- Week 4 MATH 105

Cassandra Notetaker
Edinboro University of Pennsylvania
GPA 4.0

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Notes covering factoring, special products, etc.
COURSE
College Algebra
PROF.
Dr. Phillip Funtulis
TYPE
Class Notes
PAGES
3
WORDS
CONCEPTS
factoring, special products, Math, Algebra
KARMA
25 ?

## Popular in Mathematics (M)

This 3 page Class Notes was uploaded by Cassandra Notetaker on Saturday February 13, 2016. The Class Notes belongs to MATH 105 at Edinboro University of Pennsylvania taught by Dr. Phillip Funtulis in Spring 2016. Since its upload, it has received 25 views. For similar materials see College Algebra in Mathematics (M) at Edinboro University of Pennsylvania.

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Date Created: 02/13/16
Funtulis­ MATH 105 Special Products – 2/8/16 Perfect Square Trinomials: (A + B)  = A  + 2AB + B 2 2 2 2 (A ­ B)  = A  ­ 2AB + B 2 2 Ex. Keeping the above formats in mind, factor 9x  + 30xy + 25y . (3x + 5y) 2 Difference of Cubes: 3 3 2 2 (A  + B ) = (A + B) (A  ­ AB + B ) 3 3 2 2 (A  ­ B ) = (A – B) (A  + AB + B ) Factor: 3 3 3 2 2 2 27 – r  →  (3)  – (r)   →  (3 – r) (3  + 3r + r )  →  (3 – r) (9 + 3r + r ) 9 12 3 3 4 3 3 2 3 4 4 2 6 3 4 8 27z  + 64y   →  (3z )  + (4y )   →  ((3z )  – (3z )(4y ) + (4y ) )  →  (9z  – 12z y  + 16y ) Tips for Dividing Polynomials: 24 / 4 = 6 Stop when the remainder is 0 or has a degree that is less than that of the divisor. Funtulis­ MATH 105 Factoring Trinomials – 2/10/16 2 A trinomial (quadratic) with a leading coefficient of 1; ax  + bx + c, where a, b, and c are real  numbers and none of them are zero. Rules of Thumb: For non­zero a, b, and c, in which b and c are greater than zero, 2 1. ax  + bx + c = (x +   ) (x +   ) 2. ax  ­ bx + c = (x ­   ) (x ­   ) 2 3. ax  + bx ­ c = (x +   ) (x ­   ) 4. ax  ­ bx ­ c = (x +   ) (x ­   ) To factor x  + 7x + 12, find numbers that both add to 7 and multiply to 12.  Answer: (x + 3) (x + 4). To factor 7x (x + y) – (x + y), factor out the Greatest Common Factor (x + y). Answer: (x + y) (7x – 1). Factoring by Grouping: Polynomial must have 4 terms Factor out the GCFs of both the first and second sets of terms. 2 2 2 2 Ex. mp  + 7m + 3p  + 21 can be split down the middle into mp  + 7m and 3p  + 21; then take the  GCF out of each binomial.  m(p  + 7) and 3(p  + 7). 2 Funtulis­ MATH 105 2 Answer: (m + 3) (p  + 7) Advice for Trial and Error: First try factors of a number that are close together. Ex. Factors of 6:  1 and 6, 2 and 3. AC Method: determine what two numbers add to b and multiply to c in the format ax  + bx + c. 2 Rewrite to have a polynomial with four terms and then factor by grouping.

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