polynomial, trinomial, constant, variable, factor

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.

Factoring Trionomials with and Without Algebra Tiles

This activity will create the polynomial, then show the intermediate steps to find the factors., If you have algebra tiles, build the equation generated.  "Click "Algebra Tiles" below to use the virtual tiles if you do not.  Make the appropriate changes in the tiles as you work through each of the steps in the solution.

Vocabulary and ("translation")

Example(s)/Translation

Explanation

algebra ("bind together)

3x + 4 = 7

The study of mathematics using letters.  The terms are the "words" of an algebraic expression or equation.

terms

6x⁴, 5x³, 4x²y, -x²,  x

Terms include numbers (numerical coefficients) and letters (variables).  Terms are connected by addition or subtraction.

monomial ("one term")

one term polynomial

binomial ("two terms")

two term polynomial

trinomial ("three terms")

three term polynomial

= 2x² + x - 1

polynomial ("many terms")

x2 + 3

5x³ + 2xy - 4

-6x⁴ + 4x3 - 7xy - 9

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

polynomial degree

3x²y³ + 3

The polynomial degree for both examples is 5.  The degree is determined by the term with the greatest power.  If there is more than one variable in a term, add the exponents to get the degree.

like terms

Like terms have the same variable(s) and the same degree for each variable.

adding like terms

2x + 3x

= (2+3)x = 5x

• Add coefficients of like terms (use the Distributive Property): 

  ax + bx = (a + b)x

• Watch your signs!!

• Remember:

x = x¹      1x = x       -1x = -x

3x² + x²

= 3x² + 1x² = (3+1)x² =4x²

= (3+5)x²y³ = 8x²y³

subtracting like terms

-

-2x - 6x

 

= +

= -2x + 6x

= (-2+6)x = 4x

• Subtract coefficients of like terms (use the Distributive Property:

ax - bx = (a - b)x

• Watch your signs!!

• Remember:

x = x¹      1x = x        -1x = -x

-

2x² - 3x²

 

= +

= 2x² + 3x²

= (2+3)x² = 5x²

= (3-4)x²y³ = -1x²y³

= -x²y³

Algebra Tile Practice:

Algebra Tile Basics

• Use all of the pieces to make a rectangle.

• To flip a rectangular tile, select it with the mouse and press the space bar.

Rules

• Big squares can't touch little squares.
• Little squares must all be together.
• Only equal length sides may touch.
• You may not lay two equally sized tiles of different colours next to each other.

AlgebraTilesPractice applet author:  Arlen Strader

Factoring Trinomials (Positive Coefficients)

Algebra Tiles - Factoring Trinomials

• Use all of the pieces to make a rectangle.
• To flip a rectangular tile, select it with the mouse and press the space bar.
• Once you have correctly arranged the tiles into a rectangle, the factors of the quadratic are the length and width of the rectangle.

Rules

• Big squares can't touch little squares.
• Little squares must all be together.
• Only equal length sides may touch.
• You may not lay two equally sized tiles of different colours next to each other.

AlgebraTiles1 applet author:  Arlen Strader

Factoring Trinomials (Positive and Negative Coefficients)

• Use all of the pieces to make a rectangle.
• To flip a rectangular tile, select it with the mouse and press the space bar.
• Once you have correctly arranged the tiles into a rectangle, the factors of the quadratic are the length and width of the rectangle.

Rules

• Big squares can't touch little squares.
• Little squares must all be together.
• Only equal length sides may touch.
• You may not lay two equally sized tiles of different color next to each other.

AlgebraTiles2 applet author:  Arlen Strader