1 definition of monomials: problems standard 10 definition of polynomials: problems polynomials...

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Definition of Monomials: Problems

STANDARD 10

Definition of Polynomials: Problems

POLYNOMIALS

Standard Form of a Polynomial: Problems

Adding Polynomials: Vertical and Horizontal Formats, problems

Adding Polynomials when a term is missing: Problems

Subtracting Polynomials: Vertical Format, problems

Subtracting Polynomials: Horizontal Format, problems

Adding Polynomials with more than one variable, problems

END SHOWPRESENTATION CREATED BY SIMON PEREZ. All rights reserved

http://www.mrperezonlinemathtutor.com/

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STANDARD 10:

Students add, subtract, multiply, and divide monomials and polynomials. Students solve multi-step problems, including word problems, by using these techniques.

ESTÁNDAR 10:

Los estudiantes suman restan, multiplican, y dividen monomios y polinomios. Los estudiantes resuelven problemas de múltiples pasos, incluyendo problemas escritos, usando estas técnicas.

PRESENTATION CREATED BY SIMON PEREZ. All rights reserved


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STANDARD 10

MONOMIALS:

9 4x 3pq3 14

xy

These are examples of monomials:

A monomial is a number, a variable, or the product of a number and one or more variables with whole number exponents.

The degree of a monomial is the sum of the exponents of the variables in the monomial.

Find the degree of the following monomials:

x 6

r t4 6

x y z3 5 4

x yz2 2

20

6

4 + 6 = 10

3 + 5 +4 = 12

= 20x00

x y z2 21= 2 + 1 + 2 = 5



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STANDARD 10

POLYNOMIALS:

A polynomial is a monomial or a sum of monomials.

The degree of a polynomial in one variable is the largest exponent of that variable.

Polynomials are also identified by number of terms.

POLYNOMIAL DEGREE IDENTIFIED BY DEGREE

IDENTIFIED BY NUMBER OF TERMS

5 0 constant monomial

16y +31 linear binomial

x - 3x + 92 2 quadratic trinomial

4z – 9z - 223 3 cubic trinomial



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STANDARD 10

POLYNOMIALS:

Polynomials are most commonly written in STANDARD FORM, that is in decreasing order, from largest exponent to smallest exponent.

Write the following polynomials in STANDARD FORM:

-3x + x - 22 -3x + x - 221 x0 x -3x -22

3x – x + 4x + 1 - x2 3 4 -x - x + 3x + 4x - 14 3 2 1

-x - x + 3x + 4x - 14 3 2

6x + 2x -x + 253 2 x40 x102x + + 6x – x + + 25 3 2 x0

2x + 6x – x + 25 3 2

8x + 5x + 3x -x + 76 3 4 8x + + 3x + 5x + - x + 76 4 3x50 x20 1

8x + 3x + 5x - x + 76 4 3

x0

x0



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STANDARD 10

ADDING POLYNOMIALS:

VERTICAL FORMAT:

Find the sums of the following polynomial:

(4x + 5x -3) + (3x -x + 10)2 2

24x + 5x - 323x - x + 101

+ 7+ 4x7x 2

HORIZONTAL FORMAT:

24x + 5x - 3 + 23x - x + 10 = 4x + 3x + 5x -1x -3 +102 2

= 7x + 4x + 72



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STANDARD 10

ADDING POLYNOMIALS:

VERTICAL FORMAT:

Find the sums of the following polynomial:

(5x + 2x -4) + (4x +7x + 12)

2 2

25x + 2x - 424x + 7x + 12

+ 8+ 9x9x 2

HORIZONTAL FORMAT:

25x + 2x - 4 + 24x +7x + 12 = 5x + 4x + 2x +7x -4 +122 2

= 9x + 9x + 82



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STANDARD 10

ADDING POLYNOMIALS:

Find the sums of the following polynomials using VERTICAL FORMAT:

(3x - 5) + (9x + 2x + 11)

2 2

29x + 2x +11

3x + 0x - 52

+ 6+ 2x12x 2

(4x + 7x + x + 3) + ( 2x - x + 4 – 3x )4 3 2 3 4

4x + 7x + 1x + 0x + 34 3 2

-3x + 2x + 0x - 1x + 44 3 2

+ 7- x+ x2+ 9x3 x4


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STANDARD 10

ADDING POLYNOMIALS:

Find the sums of the following polynomials using HORIZONTAL FORMAT:

(3x - 5) + (9x + 2x + 11)

2 2

29x + 2x +113x - 52

(4x + 7x + x + 3) + ( 2x - x + 4 – 3x )4 3 2 3 4

4x + 7x + x + 34 3 2 -3x + 2x -x + 44 3

+ = 3x + 9x + 2x – 5 + 11 2 2

+ 6+ 2x12x 2=

+

+ 7- x+ x2+ 9x3 x4=

= 4x – 3x +7x +2x + x -x + 3 + 444 3 3 2


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STANDARD 10

SUBTRACTING POLYNOMIALS:

Find the difference of the following polynomials using VERTICAL FORMAT:

(6x - 2) - (8x + 4x + 14)2 2

28x + 4x +14

6x + 0x - 22

-16- 4x-2x 2

(9x + 5x + 2x + 5) - ( 4x - 2x + 7 – 6x )4 3 2 3 4

9x + 5x + 2x + 0x + 54 3 2

-6x + 4x + 0x - 2x + 74 3 2

- 2+2x+ 2x2 + x3 15x 4

-

2-8x - 4x -14

6x + 0x - 22-

9x + 5x + 2x + 0x + 54 3 2

6x - 4x - 0x + 2x - 74 3 2


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STANDARD 10

SUBTRACTING POLYNOMIALS:

Find the differences of the following polynomials using HORIZONTAL FORMAT:

(4x - 5) - (8x + 3x + 10)2 2

28x + 3x +104x - 52

(5x + 6x + x + 4) - ( 3x - x + 5 – 2x )4 3 2 3 4

5x + 6x + x + 44 3 2 -2x + 3x -x + 54 3

= 4x - 8x - 3x – 5 - 10 2 2

- 15- 3x-4x 2=

- 1+ x+ x2+ 3x3 7x4=

= 5x + 2x + 6x - 3x + x + x + 4 - 544 3 3 2

- 28x - 3x -104x - 52= -

- 5x + 6x + x + 44 3 2 +2x - 3x + x - 54 3=


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It is possible to add or subtract terms of a polynomial only if they are LIKE TERMS:

Simplify 5xy + 6z x -9xy + 10z x – 15z5 5 3

5xy + 6z x -9xy + 10z x – 15z5 5 3

Simplify -8a b c + 7b c - 3b c + a b c3 5 3 53 52 5

-8a b c + 7b c - 3b c + a b c3 5 3 53 52 5 = -8a b c + a b c + 7b c – 3b c3 5 3 5 3 52 5

= -7a b c + 7b c -3b c3 5 3 52 5

= -7a b c - 3b c +7b c3 5 2 53 5

= 5xy – 9xy + 6z x + 10z x -15z5 5 3

= -4xy +16z x – 15z5 3

STANDARD 10

ADDING POLYNOMIALS:


1 definition of monomials: problems standard 10 definition of polynomials: problems polynomials...

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