Solution:
Out of the four options given we will try to factorize each one of them using Splitting of middle of term that is term containing x, method:
1. [tex]x^2 - 2 x - 8=x^2 - 4 x + 2 x -8= x\times (x-4) +2 \times (x-4)=(x+2)(x-4)[/tex]
2. [tex]x^2 + 2 x - 8=x^2 + 4 x - 2 x -8= x\times (x+4) -2 \times (x+4)=(x-2)(x+4)[/tex]
3. [tex]x^2 - 2 x - 4[/tex]= There will be no integral root.
4. [tex]x^2 + 2 x - 4[/tex]= There will be no integral root.
In Case 1, and Case 2, one of the root is negative.So,we can represent one root by a rectangle or square of different color,and another root by a rectangle or square of different color than first one.
So, Option (1) →x² - 2 x - 8 and Option (2)→ x² + 2 x - 8 are two polynomials which has been factored using algebra Tiles.
