Presentation is loading. Please wait.

Presentation is loading. Please wait.

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 + 28 3b –

Published byGarry Sutton Modified over 8 years ago

Similar presentations

Presentation on theme: "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 + 28 3b –"— Presentation transcript:

1 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 + 28 3b – 4 STEP 2 Multiply by 3b. b 2 + 6b – 7 3b – 4 – 4b 2 – 24b + 28 3b 3 + 18b 2 – 21b

2 Multiply polynomials vertically EXAMPLE 3 STEP 3 Add products. b 2 + 6b – 7 3b – 4 – 4b 2 – 24b + 28 3b 3 + 18b 2 – 21b 3b 3 + 14b 2 – 45b + 28

3 Multiply polynomials horizontally EXAMPLE 4 Find the product (2x 2 + 5x – 1)(4x – 3). (2x 2 + 5x – 1)(4x – 3) Write product. = 2x 2 (4x – 3) + 5x(4x – 3) – 1(4x – 3) = 8x 3 – 6x 2 + 20x 2 – 15x – 4x + 3 Distributive property = 8x 3 + 14x 2 – 19x + 3 Combine like terms. FOIL PATTERN The letters of the word FOIL can help you to remember how to use the distributive property to multiply binomials. The letters should remind you of the words First, Outer, Inner, and Last.

4 Multiply polynomials horizontally EXAMPLE 4 (2x + 3)(4x + 1) First OuterInner Last = 8x 2 + 2x + 12x + 3

5 Multiply binomials using the FOIL pattern EXAMPLE 5 Find the product (3a + 4)(a – 2). (3a + 4)(a – 2) = (3a)(a) + (3a)(– 2) + (4)(a) + (4)(– 2) Write products of terms. = 3a 2 + (– 6a) + 4a + (– 8) Multiply. = 3a 2 – 2a – 8 Combine like terms.

6 GUIDED PRACTICE for Examples 3, 4, and 5 Find the product. SOLUTION STEP 1 Multiply by 2 x 2 + 2x + 1 2x 2 + 4x + 2 x + 2 STEP 2 Multiply by x x 2 + 2x + 1 x + 2 2x 2 + 4x + 2 (x 2 + 2x +1)(x + 2)4 x 3 + 2x 2 + x

7 GUIDED PRACTICE for Examples 3, 4, and 5 STEP 3 Add products. x 2 + 2x + 1 x + 2 2x 2 + 4x + 2 x 3 + 2x 2 + x x 3 + 4x 2 + 5x + 2

8 GUIDED PRACTICE for Examples 3, 4, and 5 Find the product. Write product. = 3y 2 (2y – 3) – y(2y – 3) + 5(2y – 3) = 6y 3 – 9y 2 – 2y 2 + 3y + 10y – 15 Distributive property = 6y 3 – 11y 2 + 13y – 15 Combine like terms. (3y 2 –y + 5)(2y – 3) SOLUTION (3y 2 –y + 5)(2y – 3) 5

9 GUIDED PRACTICE for Examples 3, 4, and 5 Find the product. SOLUTION (4b –5)(b – 2) 6 = (4b)(b) + (4b)(– 2) + (–5)(b) + (–5)(– 2) Write products of terms. = 4b 2 – 8b – 5b + 10 Multiply. = 4b 2 – 13b + 10 Combine like terms.

Download ppt "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 + 28 3b –"

Similar presentations

Simplify the expression. 1.(–3x 3 )(5x) ANSWER –15x 4 ANSWER –9x–9x 2. 9x – 18x 3. 10y 2 + 7y – 8y 2 – 1 ANSWER 2y 2 + 7y – 1.

Simplify the expression. 1.(–3x 3 )(5x) ANSWER –15x 4 ANSWER –9x–9x 2. 9x – 18x 3. 10y 2 + 7y – 8y 2 – 1 ANSWER 2y 2 + 7y – 1.
4.5 Multiplying Polynomials

4.5 Multiplying Polynomials
Objective: To be able to find the product of two binomials. Objective: To be able to find the product of two binomials. 8.7 Multiplying Polynomials Part.

Objective: To be able to find the product of two binomials. Objective: To be able to find the product of two binomials. 8.7 Multiplying Polynomials Part.
Multiplication of Polynomials.  Use the Distributive Property when indicated.  Remember: when multiplying 2 powers that have like bases, we ADD their.

Multiplication of Polynomials.  Use the Distributive Property when indicated.  Remember: when multiplying 2 powers that have like bases, we ADD their.
Objective - To multiply polynomials. Multiply the polynomial by the monomial. 1) 3(x + 4) 2) 3) Distributive Property.

Objective - To multiply polynomials. Multiply the polynomial by the monomial. 1) 3(x + 4) 2) 3) Distributive Property.
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.

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.
Warm-Up Exercises 1. Simplify –2 (9a – b). ANSWER –18a + 2b ANSWER r3s4r3s4 2. Simplify r 2 s rs 3.

Warm-Up Exercises 1. Simplify –2 (9a – b). ANSWER –18a + 2b ANSWER r3s4r3s4 2. Simplify r 2 s rs 3.
© William James Calhoun, 2001 9-7: Multiplying Polynomials OBJECTIVES: The student will (1) use the FOIL method to multiply two binomials, and (2) multiply.

© William James Calhoun, : Multiplying Polynomials OBJECTIVES: The student will (1) use the FOIL method to multiply two binomials, and (2) multiply.
Polynomial Terms and Operations. EXAMPLE 1 Add polynomials vertically and horizontally a. Add 2x 3 – 5x 2 + 3x – 9 and x 3 + 6x 2 + 11 in a vertical.

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.
Warm-Up Exercises Factor out a common binomial EXAMPLE 1 2x(x + 4) – 3(x + 4) a. 3y 2 (y – 2) + 5(2 – y) b. Factor – 1 from ( 2 – y ). Distributive property.

Warm-Up Exercises Factor out a common binomial EXAMPLE 1 2x(x + 4) – 3(x + 4) a. 3y 2 (y – 2) + 5(2 – y) b. Factor – 1 from ( 2 – y ). Distributive property.
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.

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.
There are three techniques you can use for multiplying polynomials. The best part about it is that they are all the same! Huh? Whaddaya mean? It’s all.

There are three techniques you can use for multiplying polynomials. The best part about it is that they are all the same! Huh? Whaddaya mean? It’s all.
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.

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.
Multiplying Polynomials

Multiplying Polynomials
Do Now: 1. 2x 3  x 3 = ________ 2. 2x 3  3x 2 = ________ 3. 2x 3  (-2x) = ________ 4. 2x 3  5 = ________.

Do Now: 1. 2x 3  x 3 = ________ 2. 2x 3  3x 2 = ________ 3. 2x 3  (-2x) = ________ 4. 2x 3  5 = ________.
Objective: The student will be able to: multiply two polynomials using the FOIL method, Box method, and the distributive property.

Objective: The student will be able to: multiply two polynomials using the FOIL method, Box method, and the distributive property.
Polynomials and Factoring Polynomials and Factoring Multiplying Binomials Delores Fitch Algebra 1 Tech 504 Multimedia for Teachers.

Polynomials and Factoring Polynomials and Factoring Multiplying Binomials Delores Fitch Algebra 1 Tech 504 Multimedia for Teachers.
Review Operations with Polynomials December 9, 2010.

Review Operations with Polynomials December 9, 2010.
Multiplying Polynomials.  1. Use FOIL method if you have 2 Binomials. ◦ F (first) O (outer) I (inner) L (last)  2. Use Distribution otherwise.  Remember.

Multiplying Polynomials.  1. Use FOIL method if you have 2 Binomials. ◦ F (first) O (outer) I (inner) L (last)  2. Use Distribution otherwise.  Remember.
Lesson 7-7 Multiplying Polynomials

Lesson 7-7 Multiplying Polynomials

Similar presentations

Ads by Google