Chapter 8.4, Problem 7CB

To determine

To explain: The reason algebra of tiles cannot be used to represent the given trinomial as a rectangle.

Answer to Problem 7CB

The given polynomial $x^2+2x+3$ .cannot be factored, therefore using tiles algebra it cannot be represented as a rectangle.

Explanation of Solution

Given information:

The given trinomial is $x^2+2x+3$ .

Concept used:

A factorable polynomial can be represented as a rectangle, using tiles algebra.

For example: The polynomial $x^2+5x+6$ can be factorized as $x^2+5x+6=\left(x+2\right)\left(x+3\right)$ can be represented by one $x^2$ tile, five x tiles and six unit ( +) tiles as shown in Figure here:

  

Each factor represents one side of the rectangle.

Calculations:

The given polynomial $x^2+2x+3$ .cannot be factored rationally.

Since, the given polynomial $x^2+2x+3$ .cannot be factored rationally, hence it cannot be represented b as a rectangle.

Conclusion:

The given polynomial $x^2+2x+3$ .cannot be factored, therefore using tiles algebra it cannot be represented as a rectangle.