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

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. $x^2 - 2 x - 8=x^2 - 4 x + 2 x -8= x\times (x-4) +2 \times (x-4)=(x+2)(x-4)$

2. $x^2 + 2 x - 8=x^2 + 4 x - 2 x -8= x\times (x+4) -2 \times (x+4)=(x-2)(x+4)$

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.

Answer 2

Answer:

x2 – 2x – 8 option 1