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Grade 9:  The Learning Equation Math

22.06 Terms of Polynomials

 Variables and Equations Refresher pp 42-3

 SeekAWord2ech.class Author Prerequisite Skills:

Learning Outcomes:      Review     Enrichment      Key Terms     Prerequisite Skills

The student will:

 Term Model Coefficient Variable 3x2 variable terms 3 x -3x2 -3 x 5x 5 x -5x -5 x 3 constant terms no coefficient or variable -3 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

stands for the number 1

stands for negative 1

stands for a number

stands for the negative of a number

half of a number         third of a number        quarter of a number

stands for square of a number

stands for negative square of a number

Vocabulary

Example(s)/Models

Explanation/"Translation"

monomial

-12, 15x0y0, 6x4, -x2,  x

"one term" polynomial

= 3

= x

= 3x

= 2x2

= -2x2

binomial

x2 + 3, 3y3 - 2x

"two term" polynomial

= 3x - 2

= x + 1

= x2 + 2x

= -x2 - 3

trinomial

5x3 + 2xy - 4

"three term" polynomial

 = 2x2 + x - 1 = x2 + x + 1 = 2x2 + 5x + 3 = -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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