6.1 Factoring Polynomials

Slides:

Advertisements

Similar presentations

TWO STEP EQUATIONS 1. SOLVE FOR X 2. DO THE ADDITION STEP FIRST

Advertisements

Products and Factors of Polynomials

More with Exponents and Scientific Notation MATH 017 Intermediate Algebra S. Rook.

Factoring Polynomials

September 8, 2011 "The way to be nothing is to do nothing." -- Nathaniel Howe Test prep, p. 18 #

FACTORS OF INTEGERS AND POLYNOMIALS Section x 4 + 3x 3 + 9x 8 – 15x 5 + 2x 14 Polynomial Coefficients Leading Coefficient Leading Term Degree of.

§ 1.10 Properties of the Real Number System. Angel, Elementary Algebra, 7ed 2 Commutative Property Commutative Property of Addition If a and b represent.

BELL RINGER MM1A2c & MM1A1h Find the sum or difference.

Multiplying Powers Dividing Powers Zero ExponentsNegative.

Adding and Subtracting Polynomials 7-6

Solving Two-Step Equations

Jeopardy Q 1 Q 6 Q 11 Q 16 Q 21 Q 2 Q 7 Q 12 Q 17 Q 22 Q 3 Q 8 Q 13

Exponents You will have 20 seconds to complete each of the following 16 questions. A chime will sound as each slide changes. Read the instructions at.

= (x + 6) (x + 2) 1. x2 +8x x2 +16x + 48 = (x + 12) (x + 4)

ALGEBRAIC EXPRESSIONS

DIVIDING INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.

MULTIPLYING MONOMIALS TIMES POLYNOMIALS (DISTRIBUTIVE PROPERTY)

SUBTRACTING INTEGERS 1. CHANGE THE SUBTRACTION SIGN TO ADDITION

MULT. INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.

FACTORING Think Distributive property backwards Work down, Show all steps ax + ay = a(x + y)

C1 Sequences and series. Write down the first 4 terms of the sequence u n+1 =u n +6, u 1 =6 6, 12, 18, 24.

Objective - To simplify expressions using the order of operations. Simplify each expression below. 1) 6 + 5(8 - 2) 2) 3) 4)

Order of Operations.

Columbus State Community College

8-2 Factoring by GCF Warm Up Lesson Presentation Lesson Quiz

The Distributive Property & Combining Like Terms

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 Section 5.5 Dividing Polynomials Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1.

SYSTEMS OF EQUATIONS.

Multiply Binomials (ax + b)(cx +d) (ax + by)(cx +dy)

P.4 Factoring Polynomials

Properties of Exponents

Chapter 5 Test Review Sections 5-1 through 5-4.

Objectives The student will be able to: 1. multiply a monomial and a polynomial. SOL: A.2b Designed by Skip Tyler, Varina High School.

Multiply Binomials (ax + b)(cx +d) (ax + by)(cx +dy)

Addition 1’s to 20.

25 seconds left…...

Test B, 100 Subtraction Facts

U1A L1 Examples FACTORING REVIEW EXAMPLES.

{ Take notes on the properties at this time!! !.

Solving Fraction Equations by Multiplying

Algebra I B. MacDonald.  What is a GCF? What is a GCF?  Factoring out a GCF Factoring out a GCF.

EXAMPLE 3 Use synthetic division

Divisibility Rules Page 10 in textbook.

Exponents, Polynomials, and Polynomial Functions.

Chapter 6 Polynomial Functions and Inequalities. 6.1 Properties of Exponents Negative Exponents a -n = –Move the base with the negative exponent to the.

6.1 Factoring Polynomials Goal: To factor out a common factor of a polynomial.

Algebraic Operations. Goals Add and subtract algebraic expressions and simplify like terms by applying commutative, associative, and distributive properties.

Warm-Up 1. f( g(x)) = ____ for g(x) = 2x + 1 and f(x) = 4x , if x = 3 2. (f + g)(x) = ____ for g(x) = 3x2+ 2x and f(x) = 3x (f/g)(x)

DIVISIBILITY RULES.

Using the Distributive Property For all numbers a, b, and c, a( b + c) = ab + acand ( b + c )a = ba + ca a (b - c) = ab - acand ( b - c )a = b(a) - c(a)

Copy down the following expressions and circle the like terms. 1. 7x 2 + 8x -2y + 8 – 6x 2. 3x – 2y + 4x 2 – y 3. 6y + y 2 – 3 + 2y 2 – 4y 3 What are like.

Warm-up Answers:. Homework Answers: P3 (55-58 all, all, odds, all) /1690.

Warm up! Simplify the following 1.Paraphrase the rules for multiplying exponents? 2.What order do the exponents have to be in? 3.x 3 x 7 x x 2 4.3x 3 4x.

DIVISIBILITY RULES. A number is divisible by: If the number ends in 0 the number is also divisible by 2 and 3 the sum of the number's digits.

Unit 2: Properties of Exponents Jeopardy

8-5 Factoring Using the distributive property

Apply Exponent Properties Involving Quotients

5.2 Polynomials Objectives: Add and Subtract Polynomials

7.5 Factoring Linear Expression

Factoring Expressions 7.EE.1

Factoring Polynomials

6.1 Factoring Polynomials

Divisibility Rules.

1.5 The Distribute Property of Multiplication over Addition

Divisibility Rules.

Unit 2: Properties of Exponents Jeopardy

1.5 Distributing and Factoring

Presentation transcript:

6.1 Factoring Polynomials factor out a common factor

Factoring (Divide): Find a # and/or variable that is divisible by all #’s in the expression. To divide the variable subtract the exponents

Divisible by… 2 if last digit is an even number. 3 if the sum of the digits is divisible by 3 4 if the number formed by the last two digits is divisible by 4 5 if the number ends in 0 or 5 7 Nike Rule: “just do it” (long division) 9 if the sum of the digits  by 9 10 if the last digit is a zero.

“Factoring Polynomials” the REVERSE of the Distributive Property 5(x + 3) = 5x + 15 “Factoring Polynomials” the REVERSE of the Distributive Property

Ex 1:Factor: 10x + 15 2x + 3 Check your answer!!!!!

Ex 2 Factor: 12x + 4 3x + 1 Check your answer!!!!!

Ex 3 Factor: 18x3 + 12x 3x2 + 2 Check your answer!!!!!

Ex 4 Factor: x2 + 7x x(x + 7)

Ex 5 Factor: a2b + 2ab ab(a + 2)

Ex 6 Factor: 5x5y4 + 20xy3 5 x y3 ( ) x4y + 4 5xy3(x4y + 4)

Ex 7 Factor 16y5 + 20y3 4y3(4y2 + 5)

Ex 8 Factor: x3(9 + 25x4)

Ex 9 Factor: 3m3n(4m2n + 3m + 2n)

Ex 10 Factor: 16x(x5 - 2x4 - 3)

Ex 11 Factor: x2(6x2 - 10x + 3)

Ex 12 Factor: 2a2(2a2b4 – ab2 + 3)

Homework Page 264 ( 10-40) even