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Grade 9:  The Learning Equation Math

22.06 Terms of Polynomials

2icon.jpg (3565 bytes)

Variables and Equations

Refresher pp 42-3

 

SeekAWord2ech.class Author

Prerequisite Skills:

Key Terms          

algebra, term, constant, variable, numerical coefficient, polynomial degree, like terms

Learning Outcomes:      Review     Enrichment      Key Terms     Prerequisite Skills

The student will:

Term Model Coefficient Variable
3x2 variable terms  bigsqr.jpg (1371 bytes) bigsqr.jpg (1371 bytes) bigsqr.jpg (1371 bytes) 3 x
-3x2 bigred.jpg (1379 bytes) bigred.jpg (1379 bytes) bigred.jpg (1379 bytes) -3 x
5x longtall.jpg (1108 bytes) longtall.jpg (1108 bytes) longtall.jpg (1108 bytes) longtall.jpg (1108 bytes) longtall.jpg (1108 bytes) 5 x
-5x redtall.jpg (1206 bytes) redtall.jpg (1206 bytes) redtall.jpg (1206 bytes) redtall.jpg (1206 bytes) redtall.jpg (1206 bytes) -5 x
3 constant terms smlsqr.jpg (1028 bytes) smlsqr.jpg (1028 bytes) smlsqr.jpg (1028 bytes)

no coefficient or variable

-3 smlred.jpg (946 bytes) smlred.jpg (946 bytes) smlred.jpg (946 bytes) no coefficient or variable

 

Algebra Tile Review

Algebra tiles have a variety of other names: algetiles, math tiles, and virtual tiles.  Algebra tiles can help you visualize equivalent algebraic expressions and/or equations.  Many of the real tiles have a positive and a negative side. The virtual algebra tiles activities will use multi-coloured positive tiles. The reverse (negative) side of each of these tiles is red. It helps to understand that negative tiles have one positive and one negative dimension.

Some algebra kits use black tiles for positive areas and red for the flip (negative) sides. Click the "Black/Red Tiles" button for additional information.

 

 

Algebra Tiles and the Distributive Property

 

 

 

Full Tiles and Part Tiles

Let's start out by looking at what the algebra tiles will represent

smlsqr.jpg (1028 bytes) stands for the number 1

smlred.jpg (946 bytes) stands for negative 1

longtall.jpg (1108 bytes) stands for a number

redtall.jpg (1206 bytes) stands for the negative of a number

 wpe19E.jpg (1337 bytes) half of a number         wpe1A0.jpg (1390 bytes) third of a number        wpe1A2.jpg (1398 bytes) quarter of a number

bigsqr.jpg (1371 bytes) stands for square of a number

bigred.jpg (1379 bytes) stands for negative square of a number

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Vocabulary

Example(s)/Models

Explanation/"Translation"

monomial

-12, 15x0y0, 6x4, -x2,  x

"one term" polynomial

smlsqr.jpg (1028 bytes) smlsqr.jpg (1028 bytes) smlsqr.jpg (1028 bytes) = 3

longtall.jpg (1108 bytes) = x

longtall.jpg (1108 bytes)longtall.jpg (1108 bytes)longtall.jpg (1108 bytes) = 3x

bigsqr.jpg (1371 bytes) bigsqr.jpg (1371 bytes) = 2x2

bigred.jpg (1379 bytes) bigred.jpg (1379 bytes) = -2x2

binomial

x2 + 3, 3y3 - 2x

"two term" polynomial

longtall.jpg (1108 bytes)longtall.jpg (1108 bytes)longtall.jpg (1108 bytes) smlred.jpg (946 bytes)smlred.jpg (946 bytes) = 3x - 2

 longtall.jpg (1108 bytes)  smlsqr.jpg (1028 bytes) = x + 1

bigsqr.jpg (1371 bytes) longtall.jpg (1108 bytes) longtall.jpg (1108 bytes) = x2 + 2x

bigred.jpg (1379 bytes) smlred.jpg (946 bytes) smlred.jpg (946 bytes) smlred.jpg (946 bytes) = -x2 - 3

trinomial

5x3 + 2xy - 4

"three term" polynomial

bigsqr.jpg (1371 bytes)bigsqr.jpg (1371 bytes) longtall.jpg (1108 bytes) smlred.jpg (946 bytes) = 2x2 + x - 1
bigsqr.jpg (1371 bytes)  longtall.jpg (1108 bytes)  smlsqr.jpg (1028 bytes) = x2 + x + 1
bigsqr.jpg (1371 bytes) bigsqr.jpg (1371 bytes)
longtall.jpg (1108 bytes)longtall.jpg (1108 bytes)longtall.jpg (1108 bytes)longtall.jpg (1108 bytes)longtall.jpg (1108 bytes)
smlsqr.jpg (1028 bytes) smlsqr.jpg (1028 bytes) smlsqr.jpg (1028 bytes)
= 2x2 + 5x + 3
bigred.jpg (1379 bytes) bigred.jpg (1379 bytes)
redtall.jpg (1206 bytes)redtall.jpg (1206 bytes)redtall.jpg (1206 bytes)redtall.jpg (1206 bytes)redtall.jpg (1206 bytes)
smlred.jpg (946 bytes) smlred.jpg (946 bytes) smlred.jpg (946 bytes)
= -2x2 - 5x - 3

polynomial

15x0y0

x2 + 3

5x3 + 2xy - 4

-6x4 + 4x3 - 7xy - 9

Polynomial means "many terms" and can be used to represent any number of terms.   Polynomial is often used to represent more than three terms.

 

Review:

 

 

Enrichment:

Degree of a Polynomial

Degree Name Example
0 constant 11
1 linear 4x + 7
2 quadratic 3x2 + 4x + 5
3 cubic 4x3 + 3x + 7
4 quartic 3x4 + 2x2 + 4
5 quintic x5 + 3x + 1

Degree:  The sum of the variable exponents in a particular term (the degree of 12x3y4z2  is 3+4+2 = 9)

Polynomial Degree:  The degree of the polynomial is determined by the term with the highest degree.

 

 

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