Download presentation

Presentation is loading. Please wait.

Published byAllan Morby Modified over 3 years ago

1
Polynomials Terms and Factoring Algebra I H.S. Created by: Buddy L. Anderson Algebra I H.S. Created by: Buddy L. Anderson

2
Vocabulary / Monomial: A number, a variable or the product of a number and one or more variables / Polynomial: A monomial or a sum of monomials. / Binomial: A polynomial with exactly two terms. / Trinomial: A polynomial with exactly three terms. / Coefficient: A numerical factor in a term of an algebraic expression. / Degree of a monomial: The sum of the exponents of all of the variables in the monomial. / Monomial: A number, a variable or the product of a number and one or more variables / Polynomial: A monomial or a sum of monomials. / Binomial: A polynomial with exactly two terms. / Trinomial: A polynomial with exactly three terms. / Coefficient: A numerical factor in a term of an algebraic expression. / Degree of a monomial: The sum of the exponents of all of the variables in the monomial.

3
Vocabulary / Degree of a polynomial in one variable: The largest exponent of that variable. / Standard form: When the terms of a polynomial are arranged from the largest exponent to the smallest exponent in decreasing order. / Degree of a polynomial in one variable: The largest exponent of that variable. / Standard form: When the terms of a polynomial are arranged from the largest exponent to the smallest exponent in decreasing order.

4
Degree of a Monomial / What is the degree of the monomial? / The degree of a monomial is the sum of the exponents of the variables in the monomial. / The exponents of each variable are 4 and 2. 4+2=6. / Therefore the degree is six and it can be referred to as a sixth degree monomial. / What is the degree of the monomial? / The degree of a monomial is the sum of the exponents of the variables in the monomial. / The exponents of each variable are 4 and 2. 4+2=6. / Therefore the degree is six and it can be referred to as a sixth degree monomial.

5
Polynomial / A polynomial is a monomial or the sum of monomials / Each monomial in a polynomial is a term of the polynomial. / The number factor of a term is called the coefficient. The coefficient of the first term in a polynomial is the lead coefficient / A polynomial with two terms is called a binomial. / A polynomial with three terms is called a trinomial. / A polynomial is a monomial or the sum of monomials / Each monomial in a polynomial is a term of the polynomial. / The number factor of a term is called the coefficient. The coefficient of the first term in a polynomial is the lead coefficient / A polynomial with two terms is called a binomial. / A polynomial with three terms is called a trinomial.

6
Degree of a Polynomial in One Variable / The degree of a polynomial in one variable is the largest exponent of that variable. / The degree of this polynomial is 2, since the highest exponent of the variable x is 2. /T/The degree of a polynomial in one variable is the largest exponent of that variable. /T/The degree of this polynomial is 2, since the highest exponent of the variable x is 2.

7
Standard Form of a Polynomial / To rewrite a polynomial in standard form, rearrange the terms of the polynomial starting with the largest degree term and ending with the lowest degree term. / The leading coefficient, the coefficient of the first term in a polynomial written in standard form, should be positive. / To rewrite a polynomial in standard form, rearrange the terms of the polynomial starting with the largest degree term and ending with the lowest degree term. / The leading coefficient, the coefficient of the first term in a polynomial written in standard form, should be positive.

8
Put in Standard Form

9
Factoring Polynomials / By Grouping / Difference of Squares / Perfect Square Trinomials / X-Box Method / By Grouping / Difference of Squares / Perfect Square Trinomials / X-Box Method

10
By Grouping / When polynomials contain four terms, it is sometimes easier to group like terms in order to factor. / Your goal is to create a common factor. / You can also move terms around in the polynomial to create a common factor. / When polynomials contain four terms, it is sometimes easier to group like terms in order to factor. / Your goal is to create a common factor. / You can also move terms around in the polynomial to create a common factor.

11
By Grouping FACTOR: 3xy - 21y + 5x – 35 / Factor the first two terms: 3xy - 21y = 3y (x – 7) / Factor the last two terms: + 5x - 35 = 5 (x – 7) The terms in the parentheses are the same so it ’ s the common factor Now you have a common factor (x - 7) (3y + 5) FACTOR: 3xy - 21y + 5x – 35 / Factor the first two terms: 3xy - 21y = 3y (x – 7) / Factor the last two terms: + 5x - 35 = 5 (x – 7) The terms in the parentheses are the same so it ’ s the common factor Now you have a common factor (x - 7) (3y + 5)

12
By Grouping FACTOR: 15x – 3xy + 4y – 20 / Factor the first two terms: 15x – 3xy = 3x (5 – y) / Factor the last two terms: + 4y – 20 = 4 (y – 5) / The terms in the parentheses are opposites so change the sign on the 4 - 4 (-y + 5) or – 4 (5 - y) Now you have a common factor (5 – y) (3x – 4) FACTOR: 15x – 3xy + 4y – 20 / Factor the first two terms: 15x – 3xy = 3x (5 – y) / Factor the last two terms: + 4y – 20 = 4 (y – 5) / The terms in the parentheses are opposites so change the sign on the 4 - 4 (-y + 5) or – 4 (5 - y) Now you have a common factor (5 – y) (3x – 4)

13
Difference of Squares / When factoring using a difference of squares, look for the following three things: / only 2 terms / minus sign between them / both terms must be perfect squares / If all 3 of the above are true, write two ( ), one with a + sign and one with a – sign : ( + ) ( - ). / When factoring using a difference of squares, look for the following three things: / only 2 terms / minus sign between them / both terms must be perfect squares / If all 3 of the above are true, write two ( ), one with a + sign and one with a – sign : ( + ) ( - ).

14
Try These 1. a 2 – 16 2. x 2 – 25 3. 4y 2 – 16 4. 9y 2 – 25 5. 3r 2 – 81 / 6. 2a 2 + 16 1. a 2 – 16 2. x 2 – 25 3. 4y 2 – 16 4. 9y 2 – 25 5. 3r 2 – 81 / 6. 2a 2 + 16

15
Perfect Square Trinomials / When factoring using perfect square trinomials, look for the following three things: / 3 terms / last term must be positive / first and last terms must be perfect squares / If all three of the above are true, write one ( ) 2 using the sign of the middle term. / When factoring using perfect square trinomials, look for the following three things: / 3 terms / last term must be positive / first and last terms must be perfect squares / If all three of the above are true, write one ( ) 2 using the sign of the middle term.

16
Try These 1. a 2 – 8a + 16 / 2. x 2 + 10x + 25 / 3. 4y 2 + 16y + 16 / 4. 9y 2 + 30y + 25 5. 3r 2 – 18r + 27 / 6. 2a 2 + 8a - 8 1. a 2 – 8a + 16 / 2. x 2 + 10x + 25 / 3. 4y 2 + 16y + 16 / 4. 9y 2 + 30y + 25 5. 3r 2 – 18r + 27 / 6. 2a 2 + 8a - 8

17
X-Box Method / No, we are not going to feed polynomials into a game system that will factor them. / We will go over the following example. / No, we are not going to feed polynomials into a game system that will factor them. / We will go over the following example.

18
X-Box Method -13 (3)(-10)= -30 -15 2 -10 -15x 2x 3x 2 x-5 3x +2 3x 2 -13x -10 = (x-5)(3x+2)

19
X-Box Method / The color codes in the equation show where the numbers go in the diamond and box. / The -15 and 2 came from the fact that you needed 2 numbers that multiplied to get -30 and added to get -13. / The color codes in the equation show where the numbers go in the diamond and box. / The -15 and 2 came from the fact that you needed 2 numbers that multiplied to get -30 and added to get -13.

20
X-Box Method / The outside of the box are the GCF of what they are above or beside. / These give you you r 2 factors. / The outside of the box are the GCF of what they are above or beside. / These give you you r 2 factors.

Similar presentations

Presentation is loading. Please wait....

OK

Day 1 – Polynomials Multiplying Mrs. Parziale

Day 1 – Polynomials Multiplying Mrs. Parziale

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Download ppt on cybercrime in india Ppt on various properties of air Ppt on windows vista operating system Ppt on harmful effects of fast food Ppt on kisan call centre Free download ppt on social networking sites Download ppt on indus valley civilization for kids Ppt on superconductors applications Ppt on remote operated spy robot technology Ppt on marketing management for class 12