Preparation:
1. prepare Algebra Tiles
2. Square tiles of dimension 10 X 10 each, representing x^2.•
3. Rectangular tiles of dimension 10 X 1 each , representing x .
4. Square tiles of dimension 1 X 1 each representing 1.·
Assumption:
We have assumed that
1. In the rectangular tiles each of dimension x sq units the top side represents (+ x) and the bottom side represents (- x).
2.Similarly in the square tiles each of dimension 1 sq unit the top side represents (+1) and the bottom side represents (-1).·
PROCEDURE
I) Representation of x^2 +5x + 6·
To represent this we need 1 square tile representing x^2 , 5 algebra tiles representing x and 6 algebra tiles representing 1.·
By splitting the middle term of the given polynomial we get the expression x^2 +3x +2x + 6.· Place a square tile of dimension 10X10 representing x^2 .·
Add 3 tiles of dimension 10 X 1 each to any side of the tile x^2.The area of new shape formed represents x^2 +3x.· Add 2 tiles of dimension 10 X 1 each to the side adjacent to the previous side.
The area of new shape formed represents x^2 +3x+2x.· Add 6 tiles of dimension 1 X 1 each to complete the rectangle.
The area of new shape formed represents x^2 +3x+2x+6.
II) Representation of x^2 -x - 6·
To represent this we need 1 square tile representing x^2 , 5 algebra tiles representing x and 6 algebra tiles representing 1.·
By splitting the middle term of the given polynomial we get the expression x^2 -3x +2x - 6.· Place a square tile of dimension 10X10 representing x^2 .·
Add 2 tiles of dimension 10 X 1 each to any side of the tile x^2.The area of new shape formed represents x^2 +2x.· Subtract 3 tiles of dimension 10 X 1 each to the side adjacent to the previous side.
The area of new shape formed represents x^2 +2x-3x.· Subtract 6 tiles of dimension 1 X 1 each to complete the rectangle.
The area of new shape formed represents x^2 +2x-3x-6
III) Representation of x^2 -5x + 6·
To represent this we need 1 square tile representing x2 , 5 algebra tiles representing x and 6 algebra tiles representing 1.·
By splitting the middle term of the given polynomial we get the expression x^2 -3x -2x + 6.·
Place a square tile of dimension 10X10 representing x^2 .· Subtract 3 tiles of dimension 10 X 1 each to any side of the tile x^2.
The area of new shape formed represents x^2 -3x.· Add 6 tiles of dimension 1 X 1 each to get 2 tiles of dimension 10 X 1 each to the side adjacent to the previous side.
The area of new shape formed represents x^2 -3x+6.· Subtract 2 tiles of dimension 10 X 1 each to complete the rectangle.
The area of new shape formed represents x^2 -3x+6-2x.
IV) Representation of x^2 +x -6·
To represent this we need 1 square tile representing x^2 , 5 algebra tiles representing x and 6 algebra tiles representing 1.·
By splitting the middle term of the given polynomial we get the expression x^2 +3x -2x - 6.·
Place a square tile of dimension 10X10 representing x^2 .·
Add 3 tiles of dimension 10 X 1 each to any side of the tile x2.The area of new shape formed represents x^2 +3x.· Subtract 2 tiles of dimension 10 X 1 each from the side adjacent to the previous side.
The area of new shape formed represents x^2 +3x-2x.· Subtract 6 tiles of dimension 1 X 1 each to complete the rectangle.
The area of new shape formed represents x^2 +3x-2x-6.
· Observation· In the representation of x^2 +5x + 6 , a rectangle is formed whose sides are (x+3) and (x+2) which are the factors of it.· In the representation of x^2 -x - 6 , a rectangle is formed whose sides are (x-3) and (x+2) which are the factors of it.· In the representation of x^2 -5x + 6 , a rectangle is formed whose sides are (x-3) and (x-2) which are the factors of it.· In the representation of x^2 +x - 6 , a rectangle is formed whose sides are (x+3) and (x-2) which are the factors of it.
Result:Thus we have observed that in all the four cases a rectangle is formed whose sides are the factors of the given polynomial.
No comments:
Post a Comment