Chapter 1.6, Problem 13CB

Solution

a.

To use algebra tiles to form a rectangle with area $2x+6$ and represent the equation in factored form.

Equation in factored form $=2(x+3)$

Given:

The area of model $2x-8$

  

The factored form from the rectangle can be written as: $2(x-4)$

The equation: $2x+6$

Calculation:

  $2x+6$

can be represented by using algebra tiles to form a rectangle as shown:

  

The factored form from the rectangle can be written as: $2(x+3)$

Conclusion:

The factored form of equation $2x+6$ using algebra tiles $=2(x+3)$

b.

To use algebra tiles to form rectangles to represent each area in the table and represent each equation in factored form.

Equation	Factored Form
$2x+6$	$2(x+3)$
$3x+3$	$3(x+1)$
$3x-12$	$3(x-4)$
$5x+10$	$5(x+2)$

Given:

The area of model $2x-8$

  

The factored form from the rectangle can be written as: $2(x-4)$

The equation: $2x+6$ , $3x+3$ , $3x-12$ , $5x+10$

Calculation:

  $2x+6$

can be represented by using algebra tiles to form a rectangle as shown:

  

The factored form from the rectangle can be written as: $2(x+3)$

  $3x+3$

can be represented by using algebra tiles to form a rectangle as shown:

  

The factored form from the rectangle can be written as: $3(x+1)$

  $3x-12$

can be represented by using algebra tiles to form a rectangle as shown:

  

The factored form from the rectangle can be written as: $3(x-4)$

  $5x+10$

can be represented by using algebra tiles to form a rectangle as shown:

  

The factored form from the rectangle can be written as: $5(x+2)$

Conclusion:

The factored form of equations using algebra tiles:

Equation	Factored Form
$2x+6$	$2(x+3)$
$3x+3$	$3(x+1)$
$3x-12$	$3(x-4)$
$5x+10$	$5(x+2)$

c.

To explain the procedure to find the factored form of an expression.

Consider an example of equation $=4x+12$

Now, carry out prime factorization of each term

The prime factorization of term $4x$ is: $2\times 2\times x$

The prime factorization of term $12$ is: $2\times 2\times 3$

The common factors of the two terms: $2\times 2$

Take these factors common $=2\times 2\times (x+3)$

Hence the factored form of the equation $=4(x+3)$