Question

A polynomial is factored using algebra tiles. Which polynomial was factored? X2 – 2x – 8 x2 + 2x – 8 x2 – 2x – 4 x2 + 2x – 4

Answer 1

x2 – 2x – 8 option 1

Answer 2

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.
`x^2 - 2 x - 8=x^2 - 4 x + 2 x -8= x* (x-4) +2 * (x-4)=(x+2)(x-4)`

2.
`x^2 + 2 x - 8=x^2 + 4 x - 2 x -8= x* (x+4) -2 * (x+4)=(x-2)(x+4)`

3.
`x^2 - 2 x - 4`= There will be no integral root.

4.
`x^2 + 2 x - 4`= 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.