Polynomials a variable expression whose terms are Monomials. - - PowerPoint PPT Presentation

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Polynomials a variable expression whose terms are Monomials. - - PowerPoint PPT Presentation

Sep 25, 2022 14 likes •176 views

D AY 131 P OLYNOMIAL O PERATIONS V OCABULARY Monomial a Number, a Variable or a PRODUCT of a number and a variable. * monomials cannot have radicals with variables inside, quotients of variables or variables with negative exponents.

SLIDE 1

DAY 131 – POLYNOMIAL OPERATIONS

SLIDE 2

VOCABULARY

Monomial – a Number, a Variable or a PRODUCT

f a number and a variable.

* monomials cannot have radicals with variables inside, quotients of variables or variables with negative exponents. Degree of a monomial – is the SUM of the exponents of the variable(s) in the monomial. The degree of constant term is 0.

SLIDE 3

Polynomials – a variable expression whose terms are Monomials. Monomials have 1 term. Binomials have 2 terms. Trinomials have 3

terms. Polynomials with more than 3 terms do

not have special names. Polynomials in one variable are usually arranged in descending

rder so that the exponents of the variables

decrease from left to right. *polynomials(just like monomials) cannot have radicals with variables inside, quotients of variables or variables with negative exponents.

SLIDE 4

Degree of polynomial – is the Greatest of the degrees of any of its terms. (Remember each term is a monomial so the degree will be the sum of the exponents in the monomial.) Constant Term of Polynomial – Term that does not have a variable attached to it. Leading Coefficient of Polynomial – is the coefficient of the variable with the largest exponent.

SLIDE 5

Evaluate Polynomials – just substitute in the assigned value for the variable and find the value of the polynomial. Example: The value will be 45.

. 3 evaluate 6 4 3 2    x x x

. 45 6 ) 3 ( 4 ) 3 ( 3

2

  

SLIDE 6

Add Polynomials – to add polynomials just Combine like

terms. There are 2 formats you can use to add

polynomials – horizontal format or vertical format. Example: Horizontal Format: Vertical Format

4 6 10 ) 2 2 7 ( ) 6 4 3 (

2 2 2

        x x x x x x ) 6 4 3 (

2

  x x

) 2 2 7 (

2

   x x

4 6 10 2   x x

SLIDE 7

Subtract Polynomials – To subtract polynomials just Add the additive inverse of the 2nd polynomial. There are 2 formats you can use to subtract polynomials – horizontal format or vertical format. Example: Horizontal Format: Vertical Format

8 2 4 ) 2 2 7 ( ) 6 4 3 (

2 2 2

         x x x x x x ) 6 4 3 (

2

  x x

) 2 2 7 (

2

   x x

8 2 4

2

   x x

SLIDE 8

IN EACH PYRAMID EACH BLOCK IS THE SUM OF THE

TWO BLOCKS BELOW. FILL IN THE MISSING EXPRESSIONS.

1. 2.

SLIDE 9

IN EACH PYRAMID EACH BLOCK IS THE SUM OF THE

TWO BLOCKS BELOW. FILL IN THE MISSING EXPRESSIONS.

1. 2.

SLIDE 10

3. 4.

SLIDE 11

3. 4.

SLIDE 12

5. 6.

SLIDE 13

5. 6.

SLIDE 14

7. 8.

SLIDE 15

7. 8.

SLIDE 16

7. 8.