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# P1-2 Operations on Polynomials

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Tweet## Emily Quon

on 15 October 2012#### Transcript of P1-2 Operations on Polynomials

Classification of Polynomials Simplifying Polynomial

Expressions The Process of Verification The Distributive Property Using Numbers Using the Distributive Property Method to Multiply Two Polynomials Mathematics 10C

P1-2

Operations on Polynomials Monomials Naming Polynomials by the number of terms they contain 1 term is a monomial

Ex: 5y (Bi)(nomials) 2 terms is a binomial

Ex: 5x-4 (Tri)(no)(mials) 3 terms is a trinomial

Ex: (4xy)(34x)(2) (Poly)(no)(mi)(als) 4 or more terms is a polynomial

Ex: 3x+43xy-9l+20lw Naming Polynomials by Degree Degree of a Term If there is only one variable the degree is that. However, if there is more than one variable the degree is the sum.

Ex: 3x^2 The degree is 2

3x^2y^3 degree is 5 Degree of a Polynomial The degree of the polynomial is the degree of the highest term.

Ex:8x^2y – 5xy + 3 the degree is 3 Order of Operations BEDMAS Brackets

Exponents

Division

Multiplication

Addition

Subtraction Like Terms Terms with the same variables and the same exponents with those variables are like terms Addition and Subtraction of Polynomials In order to add and subtract polynomials we need to have like terms. You then add or subtract the numerical coefficient in the like term. Example:

(2x^2y^2)+(4x^2y^2)

(2+4)x^2y^2

6x^2y^2 Powers y^4 is a power. y is the base and 4 is the exponent. It is equal to y x y x y x y Multiplying and Dividing Polynomials When multiplying monomials you multiply the coefficients together and the variables together. Ex:

(2x^2)(4x^3)

6x^5 To divide monomials you divide the numerical coefficients and the variables. Ex:

10x^2y^6/2xy^3

5xy^3 When multiplying a monomial by a binomial you multiply each term of the binomial by the monomial. Ex:

(4x)(3y-2x)

4x(3y)+4x(-2x)

12xy+8x^2 When multiplying a monomial by a trinomial you multipy each term of the trinomial by the monomial.

Ex:

(4x)(3x^3+4y+2x)

4x(3x^3)+4x(4y)+4x(2x)

12x^4+16xy+8x^2

20x^6+16xy When multiplying a binomial by a binomial you use the FOIL method. (first, outer, inner, last)

Ex:

(2x+4x)(3y-3xy)

2x(3y)+2x(-3xy)+4x(3y)+4x(-3xy)

6xy-6x^2y+12xy-12x^2y

-6x^2y+18xy You can use the distributive property method to multiply any monomials, binomials, trinomials etc. Ex:

2a+3b(2a+3b+4c)

2a(2a)+2a(3b)+2a(4c+3b(2a)+3b(3b)+3b(4c) You can use the distributive property of a binomial by a binomial to multiply two two-digit numbers together. Ex:

23 x 45

(20+3)(40+5)

20(40)+20(5)+3(40)+3(5)

60+100+120+15

295 You can check your work by adding 1 in place of the variable. If you get the same answer, your answer is correct Ex:

(2x + 3)(x – 4)= (2x)(x) + (2x)(-4) + (3)(x) + (3)(-4)= 2x^2 – 8x + 3x – 12= 2x^2 – 5x – 12

[2(1)+3][(1)-4]

(5)(-3)

-15

2(1)^2-5(2)-12

2-10-12

-15

Full transcriptExpressions The Process of Verification The Distributive Property Using Numbers Using the Distributive Property Method to Multiply Two Polynomials Mathematics 10C

P1-2

Operations on Polynomials Monomials Naming Polynomials by the number of terms they contain 1 term is a monomial

Ex: 5y (Bi)(nomials) 2 terms is a binomial

Ex: 5x-4 (Tri)(no)(mials) 3 terms is a trinomial

Ex: (4xy)(34x)(2) (Poly)(no)(mi)(als) 4 or more terms is a polynomial

Ex: 3x+43xy-9l+20lw Naming Polynomials by Degree Degree of a Term If there is only one variable the degree is that. However, if there is more than one variable the degree is the sum.

Ex: 3x^2 The degree is 2

3x^2y^3 degree is 5 Degree of a Polynomial The degree of the polynomial is the degree of the highest term.

Ex:8x^2y – 5xy + 3 the degree is 3 Order of Operations BEDMAS Brackets

Exponents

Division

Multiplication

Addition

Subtraction Like Terms Terms with the same variables and the same exponents with those variables are like terms Addition and Subtraction of Polynomials In order to add and subtract polynomials we need to have like terms. You then add or subtract the numerical coefficient in the like term. Example:

(2x^2y^2)+(4x^2y^2)

(2+4)x^2y^2

6x^2y^2 Powers y^4 is a power. y is the base and 4 is the exponent. It is equal to y x y x y x y Multiplying and Dividing Polynomials When multiplying monomials you multiply the coefficients together and the variables together. Ex:

(2x^2)(4x^3)

6x^5 To divide monomials you divide the numerical coefficients and the variables. Ex:

10x^2y^6/2xy^3

5xy^3 When multiplying a monomial by a binomial you multiply each term of the binomial by the monomial. Ex:

(4x)(3y-2x)

4x(3y)+4x(-2x)

12xy+8x^2 When multiplying a monomial by a trinomial you multipy each term of the trinomial by the monomial.

Ex:

(4x)(3x^3+4y+2x)

4x(3x^3)+4x(4y)+4x(2x)

12x^4+16xy+8x^2

20x^6+16xy When multiplying a binomial by a binomial you use the FOIL method. (first, outer, inner, last)

Ex:

(2x+4x)(3y-3xy)

2x(3y)+2x(-3xy)+4x(3y)+4x(-3xy)

6xy-6x^2y+12xy-12x^2y

-6x^2y+18xy You can use the distributive property method to multiply any monomials, binomials, trinomials etc. Ex:

2a+3b(2a+3b+4c)

2a(2a)+2a(3b)+2a(4c+3b(2a)+3b(3b)+3b(4c) You can use the distributive property of a binomial by a binomial to multiply two two-digit numbers together. Ex:

23 x 45

(20+3)(40+5)

20(40)+20(5)+3(40)+3(5)

60+100+120+15

295 You can check your work by adding 1 in place of the variable. If you get the same answer, your answer is correct Ex:

(2x + 3)(x – 4)= (2x)(x) + (2x)(-4) + (3)(x) + (3)(-4)= 2x^2 – 8x + 3x – 12= 2x^2 – 5x – 12

[2(1)+3][(1)-4]

(5)(-3)

-15

2(1)^2-5(2)-12

2-10-12

-15