EXAMPLE 3 Multiply polynomials vertically and horizontally a. Multiply –2y 2 + 3y – 6 and y – 2 in a vertical format. b. Multiply x + 3 and 3x 2 – 2x +

Slides:

Advertisements

Similar presentations

5.5 and 5.6 Multiply Polynomials

Advertisements

EXAMPLE 3 Standardized Test Practice SOLUTION 8x 3 y 2x y 2 7x4y37x4y3 4y4y 56x 7 y 4 8xy 3 = Multiply numerators and denominators. 8 7 x x 6 y 3 y 8 x.

Chapter 5: Polynomials & Polynomial Functions

Perfect Square Trinomials and Difference of Perfect Squares

Chapter 6 – Polynomials and Polynomial Functions

2.3 Add, Subtract, & Multiply Polynomials p. 104 What are the two ways that you can add, subtract or multiply polynomials? Name three special product patterns.

 We use the acronym below to multiply two binomials. F – O – I – L – FIRST OUTSIDE INSIDE LAST.

Quiz Use Synthetic Substitution to evaluate: 3.What is the “end behavior” for: 2. Simplify When x = 2 In other words:

HW: 6.2 Practice Worksheet. EXAMPLE 1 Add polynomials vertically and horizontally a. Add 2x 3 – 5x 2 + 3x – 9 and x 3 + 6x in a vertical format.

5.3 Add, Subtract, and Multiply Polynomials. Add Polynomials Vertically or Horizontally Find the sum of the polynomials below: 2x 3 – 5x + 3x – 9 and.

Polynomial Terms and Operations. EXAMPLE 1 Add polynomials vertically and horizontally a. Add 2x 3 – 5x 2 + 3x – 9 and x 3 + 6x in a vertical.

How do I use Special Product Patterns to Multiply Polynomials?

6.3 Adding, Subtracting, & Multiplying Polynomials p. 338.

Multiply polynomials vertically and horizontally

SOLUTION EXAMPLE 2 Divide a polynomial by a binomial Divide x 2 + 2x – 3 by x – 1. STEP 1 Divide the first term of x 2 + 2x – 3 by the first term of x.

CHAPTER polynomials. SAT Problem of the day What is the distance between the origin and the point (-5,9)? A)5.9 B)6.7 C)8.1 D)10.3 E)11.4.

EXAMPLE 3 Multiply polynomials vertically and horizontally a. Multiply – 2y 2 + 3y – 6 and y – 2 in a vertical format. b. Multiply x + 3 and 3x 2 – 2x.

3.3 SPECIAL Factoring 12/5/2012. Perfect Squares

Polynomials. Polynomial a n x n + a n-1 x n-1 +….. + a 2 x 2 + a 1 x + a 0 Where all exponents are whole numbers – Non negative integers.

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

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.

2.3Special Products of Polynomials Square of a Binomial Pattern Multiply binomials by using F O I L.

Divide a polynomial by a binomial

GOAL: FACTOR CUBIC POLYNOMIALS AND SOLVE CUBIC EQUATIONS Section 6-5: Factoring Cubic Polynomials.

EXAMPLE 1 Find a common monomial factor Factor the polynomial completely. a. x 3 + 2x 2 – 15x Factor common monomial. = x(x + 5)(x – 3 ) Factor trinomial.

EXAMPLE 3 Multiply polynomials vertically

6.4 Multiplying/Dividing Polynomials 1/10/2014. How do you multiply 1256 by 13?

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.

Chapter 9 Final Exam Review. Add Polynomials (2x² + x³ – 1) (2x² + x³ – 1) Like Terms terms that have the same variable (2x³ – 5x² + x) + (2x³ – 5x² +

EXAMPLE 1 Add polynomials vertically and horizontally a. Add 2x 3 – 5x 2 + 3x – 9 and x 3 + 6x in a vertical format. SOLUTION a. 2x 3 – 5x 2 + 3x.

EXAMPLE 3 Multiply polynomials vertically Find the product (b 2 + 6b – 7)(3b – 4). SOLUTION STEP 1 Multiply by – 4. b 2 + 6b – 7 – 4b 2 – 24b b –

8-8 Special Products Objective: Students will be able to use special product patterns to multiply polynomials.

Adding, Subtracting, and Multiplying Polynomials 6.3 By: Garrett Horrell & Zack Olszewski.

Starter Simplify (4a -2 b 3 ) -3. Polynomials Polynomial a n x n + a n-1 x n-1 +….. + a 2 x 2 + a 1 x + a 0 Where all exponents are whole numbers –

An expression which is the sum of terms of the form a x k where k is a nonnegative integer is a polynomial. Polynomials are usually written in standard.

Quiz Use Synthetic Substitution to evaluate: 3.What is the “end behavior” for: 2. Simplify When x = 2 In other words:

Simplify the expression.

6 – 3 Adding, Subtracting and Multiplying Polynomials Day 1 Objective: Add, subtract, and multiply polynomials.

Notes Over 6.3 Adding Polynomial Horizontally and Vertically Find the sum. Just combine like terms.

6.3 Adding, Subtracting, & Multiplying Polynomials p. 338 What are the two ways that you can add, subtract or multiply polynomials? Name three special.

5.3 Notes – Add, Subtract, & Multiply Polynomials.

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.

Notes Over 10.2 Multiply binomials by using F O I L.

Objective: I will be able to:

Polynomials & Factoring

Example 2 Factor the polynomial. 12n n2 a. – 36 + = ( ) 2 n2 –

Special Products of Polynomials

Lesson 9.3 Find Special Products of Polynomials

Warm Up Subtract: Add:.

Warm Up Multiply using the F.O.I.L. or Box Method.

Section R.4 Factoring.

5.4 Multiplying Polynomials.

Chapter 6 Section 4.

Notes Over 10.3 Multiply binomials by using F O I L.

Notes Over 10.2 Multiply binomials by using F O I L.

Add, Subtract and Multiply Polynomials

Lesson 9.1 How do you add and subtract polynomials?

Essential Questions How do we use the Factor Theorem to determine factors of a polynomial? How do we factor the sum and difference of two cubes.

6.3 Adding, Subtracting, and Multiplying Polynomials

5.3 WARM-UP Decide whether the function is a polynomial function.

Objective SWBAT use special product patterns to multiply polynomials.

FACTORING SUMS and DIFFERENCES of CUBES

Multiplying binomial with polynomial

Use synthetic substitution to evaluate

(B12) Multiplying Polynomials

5.3 Add, Subtract, and Multiply Polynomials

Review Multiply (3b – 2)(2b – 3) Multiply (4t + 3)(4t + 3)

Algebra 1 Section 9.5.

Warm Up Simplify the expression by using distributive property and then combining like terms. x(x + 5) + 4(x + 5)

Multiplication: Special Cases

Presentation transcript:

EXAMPLE 3 Multiply polynomials vertically and horizontally a. Multiply –2y 2 + 3y – 6 and y – 2 in a vertical format. b. Multiply x + 3 and 3x 2 – 2x + 4 in a horizontal format. SOLUTION a. –2y 2 + 3y – 6 y – 2 4y 2 – 6y + 12 Multiply –2y 2 + 3y – 6 by –2. –2y 3 + 3y 2 – 6y Multiply –2y 2 + 3y – 6 by y –2y 3 + 7y 2 –12y + 12 Combine like terms.

EXAMPLE 3 Multiply polynomials vertically and horizontally b. (x + 3)(3x 2 – 2x + 4) = (x + 3)3x 2 – (x + 3)2x + (x + 3)4 = 3x 3 + 9x 2 – 2x 2 – 6x + 4x + 12 = 3x 3 + 7x 2 – 2x + 12

EXAMPLE 4 Multiply three binomials Multiply x – 5, x + 1, and x + 3 in a horizontal format. (x – 5)(x + 1)(x + 3) = (x 2 – 4x – 5)(x + 3) = (x 2 – 4x – 5)x + (x 2 – 4x – 5)3 = x 3 – 4x 2 – 5x + 3x 2 – 12x – 15 = x 3 – x 2 – 17x – 15

EXAMPLE 5 Use special product patterns a. (3t + 4)(3t – 4) Sum and difference = 9t 2 – 16 b. (8x – 3) 2 Square of a binomial = 64x 2 – 48x + 9 c. (pq + 5) 3 Cube of a binomial = p 3 q p 2 q pq = (3t) 2 – 4 2 = (8x) 2 – 2(8x)(3) = (pq) 3 + 3(pq) 2 (5) + 3(pq)(5)

GUIDED PRACTICE for Examples 3, 4 and 5 Find the product. 3. (x + 2)(3x 2 – x – 5) 3x 3 + 5x 2 – 7x – (a – 5)(a + 2)(a + 6) (a 3 + 3a 2 – 28a – 60) 5. (xy – 4) 3 x 3 y 3 – 12x 2 y xy – 64 ANSWER