Question

Which polynomial is represented by the algebra tiles? 2x2 – 4x – 6 2x2 + 4x + 6 –2x2 – 4x – 6 –2x2 + 4x + 6

Answer 1

Solution:

Algebra tiles means the product of two polynomials, which are sides of tiles which are in the shape of a square or a rectangle.

As, all the options are quadratic polynomials, so if we can factorize polynomial into two polynomials of degree 1,then we can say that these polynomial can be represented as sides of tiles.

Starting from Option

1.

$=2x^2 - 4x - 6\\\\ =2 x^2 - 6 x +2 x -6 \\\\=2x (x-3)+2 (x-3)\\\\ =(2 x +2)(x-3) \\\\ =2 (x+1)(x-3)$

2.

$2x^2 + 4x + 6$

Can't be factorized into linear binomial.

3.

$-2x^2 -4x - 6\\\\ -(2 x^2 + 4 x +6)$

Can't be factorized into linear binomial.

4.

$-2x^2 + 4x + 6\\\\ - 2 x^2+ 6 x - 2 x +6\\\\ - 2 x(x-3) -2(x-3)\\\\ (-2 x -2)(x-3)\\\\ -2(x+1)(x-3)$

The two polynomials which can be represented in terms of algebra tiles are

Option (1):

$=2x^2 - 4x - 6\\\\ =2 x^2 - 6 x +2 x -6 \\\\=2x (x-3)+2 (x-3)\\\\ =(2 x +2)(x-3) \\\\ =2 (x+1)(x-3)$, when x ≠3

why not option 4, because if you will substitute , values of x as a integral value ,other than 3, we get negative integer, which can't be area of tile represented in terms of variable x.