Warm-Up 5 minutes Add or subtract. 1) (5x2 + 4x + 2) + (-2x + 7 – 3x2)

Slides:

Advertisements

Similar presentations

Chapter 6 Polynomials.

Advertisements

7.1 – Multiplying Monomials. x · x = x 1 · x 1 =

Simplify each polynomial Adding and Subtracting Polynomials.

Multiplication of Polynomials.  Use the Distributive Property when indicated.  Remember: when multiplying 2 powers that have like bases, we ADD their.

5-9 Multiplying Monomials and Binomials

§ 4.5 Multiplication of Polynomials. Angel, Elementary Algebra, 7ed 2 Multiplying Polynomials To multiply a monomial by a monomial, multiply their coefficients.

Holt CA Course Multiplying Binomials Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.

Exponents and Polynomials

1 linearf (x) = mx + bone f (x) = ax 2 + bx + c, a  0quadratictwo cubicthreef (x) = ax 3 + bx 2 + cx + d, a  0 Degree Function Equation Common polynomial.

Adding and Subtracting Polynomials Section 0.3. Polynomial A polynomial in x is an algebraic expression of the form: The degree of the polynomial is n.

Polynomials P4.

1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Polynomials and Polynomial Functions Chapter 5.

Polynomials. The Degree of ax n If a does not equal 0, the degree of ax n is n. The degree of a nonzero constant is 0. The constant 0 has no defined degree.

4.6 Multiplying Polynomials. Objectives  Multiply two or more monomials  Multiply a polynomial and a monomial  Multiply a binomials by a binomial.

Multiplying Binomials Objectives: To Multiply Two Binomials FOIL To multiply the sum and difference of two expressions To square a binomial.

Multiplication: Special Cases Chapter 4.5. Sum x Difference = Difference of Two Squares (a + b)(a – b) = (a – b)(a + b) =a 2 – b 2.

Multiplying Polynomials

Multiplication of Polynomials

Warm up. FOIL Definition: Polynomial Special Names.

5.4 Multiplying Polynomials

4.2 Adding and Subtracting Polynomials Objective: To add and subtract polynomials. Warm – up: Simplify: 1) 6x + 7y + 4x2) m – 6 + 4m 3) -(5a – 2b.

4.5 Multiplying Polynomials by Monomials Objective: To multiply a polynomial by a monomial. Warm – up: Simplify: 1) x 3 ∙x 6 2) 2(a – 4) 3) 4(2y + 3) 4)

Multiplying Polynomials *You must know how to multiply before you can factor!”

Aim: How do we multiply polynomials? Do Now: Multiply the following 1. 2x(3x + 1) 2. (x – 1)(x + 2) 3. (x +2)(x 2 – 3x + 1)

Algebra 10.3 Special Products of Polynomials. Multiply. We can find a shortcut. (x + y) (x – y) x² - xy + - y2y2 = x² - y 2 Shortcut: Square the first.

2.2 Warm Up Find the sum or difference. 1. (2x – 3 + 8x²) + (5x + 3 – 8x²) 2. (x³ - 5x² - 4x) – (4x³ - 3x² + 2x – 8) 3. (x – 4) – (5x³ - 2x² + 3x – 11)

CLASSIFYING POLYNOMIALS. A _______________ is a sum or difference of terms. Polynomials have special names based on their _______ and the number of _______.

Divide a polynomial by a binomial

1.(-7) (-2) 2.(3)(-6) 3.(4)(5) 4.(-3) (4t) 5.(2)(-2x) 6.(7y)(3) 7.3(s+5) 8.4(-n+2) 9.4-(t+2) 10.3n+(2-n)

Warm-Up Collect like terms and arrange in descending order. 5 minutes 1) 4x 3 + 6x 4 – 2x 4 + 8x 2) 3x – 5x x 0 3) Evaluate 4x 3 + x 2 – 2 for x.

Problems of the Day Simplify each expression. 1. 9m 2 – 8m + 7m 2 2. (10r 2 + 4s 2 ) – (5r 2 + 6s 2 ) 3. (pq + 7p) + (6pq – 10p – 5pq) 4. (17d 2 – 4) –

Multiplying Polynomials January 29, Page #10-38 even 10) terms: 5x 3, x; coefficients: 5, 1 12) term: 7x 2 ; coeff: 7 14) monomial 16) monomial.

5.11 Multiplying Polynomials Goal: Multiply any two polynomials.

Adding and Subtracting Polynomials Multiplying Polynomials Factoring Polynomials.

Algebra 2a September 13, 2007 Chapter Five review.

1.(-7) (-2) 2.(3)(-6) 3.(4)(5) 4.(-3) (4t) 5.(2)(-2x) 6.(7y)(3) 7.3(s+5) 8.4(-n+2) 9.4-(t+2) 10.3n+(2-n) Algebra S9 Day 21.

7-1 Integer Exponents 7-2 Powers of 10 and Scientific Notation 7-3 Multiplication Properties of Exponents 7-4 Division Properties of Exponents 7-5 Fractional.

5.9 Multiplication of Monomials and Binomials How to Multiply a Mono by a Poly: Distribute the monomial by the polynomial.

Lesson 10.2 Multiplying Polynomials Objective: To multiply polynomials Multiply monomials by other polynomials by using distributive property Examples.

Objective The student will be able to: multiply two polynomials using the distributive property.

5.3C- Special Patterns for Multiplying Binomials SUM AND DIFFERENCE (a+b)(a-b) = a² - b² (x +2)(x – 2) = x² -4 “O & I” cancel out of FOIL SQUARE OF A BINOMIAL.

Adding and Subtracting Polynomials

AIM: How do we multiply and divide polynomials?

Polynomials and Polynomial Functions

Multiplication of monomial and binomials.

Polynomials and Polynomial Functions

9.7 MULTIPLYING POLYNOMIALS

Lesson 9.3 Find Special Products of Polynomials

5.2 Polynomials Objectives: Add and Subtract Polynomials

Monomials (Ex: 2x): It divides into everything…

5-9 Multiplying Monomials and Binomials

Lesson 5.3 Operations with Polynomials

13 Exponents and Polynomials.

Multiplying a Polynomial by a Monomial

Multiplying Polynomials

Multiply polynomials When multiplying powers with the same base, keep the base and add the exponents. x2  x3 = x2+3 = x5 Example 1: Multiplying Monomials.

5.11 Multiplying Polynomials

Warm-Up Add or subtract. 1) (5x2 + 4x + 2) + (-2x + 7 – 3x2)

Warm-Up 5 minutes Add or subtract. 1) (5x2 + 4x + 2) + (-2x + 7 – 3x2)

Warm Up Combine like terms: 6x – 2xy – 7z + 4 – 3y + x – 7xy + 3y xz.

Factoring Polynomials

(B12) Multiplying Polynomials

(2)(4) + (2)(5) + (3)(4) + (3)(5) =

Polynomials and Special Products

Ch Part 1 Multiplying Polynomials

Warm-up: Simplify. Put in standard form.

Multiplying Polynomials

A3 4.2a To Operate on Polynomials

Multiplication: Special Cases

Warm-Up 5 minutes Multiply. 1) (x – 3)(x – 2) 2) (6x + 5)(2x + 1)

Presentation transcript:

Warm-Up 5 minutes Add or subtract. 1) (5x2 + 4x + 2) + (-2x + 7 – 3x2) 2) (8rs – 2r2s3 – 5rs4) + (6r2s3 – 3r3s2 - 4rs) 3) (6x4 + 3x3 – 2x) – (3x4 – x3 + 4) 4) (7x3y2 – 4x2y + 5) – (2x2y + 3x3y2 – 4xy – 3)

5.2 Multiplication of Monomials and Binomials and Special Products Objectives: To multiply a monomial and a polynomial To multiply two binomials

Example 1 Multiply. 3a(6b + 7) = (3a)(6b) + (3a)(7) = 18ab + 21a

Example 2 Multiply. 2x(3x2 + x + 4) = (2x)(3x2) + (2x)(x) + (2x)(4)

Practice Multiply. 1) 4x(2x + 4) 2) 3a2(-5a3 + 2a – 7) 3) 5s(8t4 – 4s2 – 9t – 11)

FOIL Example 3 Multiply. (x + 2)(x + 3) u t s i d e i n s d e a s t i r s t = (x)(x) + (x)(3) + (2)(x) + (2)(3) = x2 + 3x + 2x + 6 = x2 + 5x + 6

Example 4 Multiply. (3x + 2)(x + 5) = (3x)(x) + (3x)(5) + (2)(x) + (2)(5) = 3x2 + 15x + 2x + 10 = 3x2 + 17x + 10

Example 5 Multiply. (4ab + 3)(2a2b + 1) = (4ab)(2a2b) + (4ab)(1) + (3)(1) = 8a3b2 + 4ab + 6a2b + 3

Practice Multiply. 1) (x + 3)(x + 4) 2) (x + 3)(x – 5)

Practice Multiply. 4) (2x2 – 3)(x – 2) 5) (6x2 + 5)(2x3 + 1) 6) (2xy + 4x)(-2y + y2)

Example 1 Multiply. (x + 6)(x – 6) = (x)(x) + (x)(-6) + (6)(x) + (6)(-6) = x2 – 6x + 6x - 36 = x2 - 36

Example 2 Multiply. (2x + 4)(2x – 4) = (2x)(2x) + (2x)(-4) + (4)(2x) + (4)(-4) = 4x2 – 8x + 8x - 16 = 4x2 - 16

Example 3 Multiply. (-3x + 4y)(-3x – 4y) = (-3x)(-3x) + (-3x)(-4y) + (4y)(-3x) + (4y)(-4y) = 9x2 + 12xy – 12xy – 16y2 = 9x2 – 16y2

Practice Multiply. 1) (x + 2)(x – 2) 2) (x2 + 7)(x2 – 7)

Example 4 Multiply. (x + 2)2 = (x + 2)(x + 2) = (x)(x) + (x)(2) + (2)(x) + (2)(2) = x2 + 2x + 2x + 4 = x2 + 4x + 4

Example 5 Multiply. (x - 3)2 = (x - 3)(x - 3) = (x)(x) + (x)(-3) + (-3)(x) + (-3)(-3) = x2 - 3x - 3x + 9 = x2 - 6x + 9

Example 6 Multiply. (2x – 3y)2 = (2x – 3y)(2x – 3y) = (2x)(2x) + (2x)(-3y) + (-3y)(2x) + (-3y)(-3y) = 4x2 - 6xy - 6xy + 9y2 = 4x2 - 12xy + 9y2

Practice Multiply. 1) (x + 3)2 2) (2x + 1)2 3) (2y + 4x)2