Chapter 8.6, Problem 56PFA

To determine

To determine the expression that represents the sides of the rectangle.

Answer to Problem 56PFA

  $(2x+5)(3x-6)$ or option $\text{(}b\text{)}$

Explanation of Solution

Given:

  $6x^2+3x-30$

Calculation:

Consider the given expression,

  $\Rightarrow 6x^2+3x-30$

First, taking out the common part,

  $\begin{array}{l}\Rightarrow 6x^2+3x-30\\ \Rightarrow 3[2x^2+x-10]\end{array}$

Now using middle term factorization method,

  $\begin{array}{l}\Rightarrow 3[2x^2+x-10]\\ \Rightarrow 3[2x^2-4x+5x-10]\\ \Rightarrow 3[2x(x-2)+5(x-2)]\\ \Rightarrow 3[(2x+5)(x-2)]\end{array}$

Now multiplying $3$ with the factorized part,

  $\begin{array}{l}\Rightarrow 3[(2x+5)(x-2)]\\ \Rightarrow (2x+5)(3x-6)\end{array}$

So the factors are the sides of the rectangle, multiplying both the factors give us the area of the rectangle.

Conclusion:

So, the sides of the rectangle are $(2x+5)(3x-6)$ , which is option (b).