Chapter 7.6, Problem 33E

To determine

To write: An expression that represents length of the school sign, describe two ways to determine area when x=3.

Answer to Problem 33E

1. $5x-2$ represents the length of the sign.
2. First way is to use the polynomial, second way is to use the factors while putting $x=3$ .

Explanation of Solution

Given information: The given expression is $15x^2-x-2$ , where $\text{'}x\text{'}$ is a variable. $(3x+1)ft$ is shown as the height of sign.

Calculation:

a)

Solving for factors,

  $15x^2-x-2=15x^2+5x-6x-2$

  $\begin{array}{l}=5x(3x+1)-2(3x+1)\\ =(5x-2)(3x+1)\end{array}$

  $(3x+1)$ is shown as the width of the sign in figure.

  $\therefore 5x-2$ represents the length of the sign.

b)

First way:

Putting $x=3$ in given trinomial,

  $15x^2-x-2$

  $=15{(3)}^2-3-2$

Evaluating powers and simplifying,

Area $=15{(3)}^2-3-2$

  $=135-3-2$

  $=130sq.ft$

Second way:

Putting $x=3$ in the factors calculated in part (a),

  $(5x-2)(3x+1)$

  $=(5(3)-2)(3(3)+1)$

  $=(13)(10)$

  $=130sq.ft$

Thus, area of the sign when x=3 is $130sq.ft$

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