Chapter 8.6, Problem 59PFA

a.

To determine

Find the sum of m and p by doing factor of the expression.

Answer to Problem 59PFA

The factor is $(22x+5)(30x+17)$ .

Explanation of Solution

Given:

It is given in the question that a city has commissioned the building of a rectangular park. The area of the park will be $660x^2+524x+85$ .

Concept Used:

In this, use the concept of factorization of the expression.

Calculation: Here, the expression is $660x^2+524x+85$ .

  $\begin{array}{l}660x^2+524x+85\\ 660x^2+204x+150x+85\\ 22x(30x+17)+5(30x+17)\\ (22x+5)(30x+17)\end{array}$

Here, $m=(22x+5),p=(30x+17)$

Conclusion:

The factor is $(22x+5)(30x+17)$ .

b.

To determine

Find the correct dimension for the expression.

Answer to Problem 59PFA

The correct factor is $(22x+5)(30x+17)$ .

Explanation of Solution

Given: It is given in the question that a city has commissioned the building of a rectangular park. The area of the park will be $660x^2+524x+85$ .

Concept Used:

In this, use the concept of doing factorization.

Calculation: Here, the expression is $660x^2+524x+85$ .

  $\begin{array}{l}660x^2+524x+85\\ 660x^2+204x+150x+85\\ 22x(30x+17)+5(30x+17)\\ (22x+5)(30x+17)\end{array}$

Conclusion:

The correct factor is $(22x+5)(30x+17)$ .

c.

To determine

Find the dimension of the pavilion.

Answer to Problem 59PFA

The dimension will be $(9x-13)(3x+1)$ .

Explanation of Solution

Given: It is given in the question that the expression of the park is $27x^2-30x-13$ .

Concept Used:

In this, use the concept of doing factorization.

Calculation:

Here, the expression is $27x^2-30x-13$ .

  $\begin{array}{l}27x^2-30x-13\\ 27x^2+9x-39x-13\\ 9x(3x+1)-13(3x+1)\\ (9x-13)(3x+1)\end{array}$

Conclusion:

The dimension will be $(9x-13)(3x+1)$ .

d.

To determine

Find the dimension of the park and the pavilion.

Answer to Problem 59PFA

The area will be $512$ .

Explanation of Solution

Given:

It is given in the question that the expression is $27x^2-30x-13$ such that $x=5$ .

Concept Used:

In this, use the concept of putting the value in the expression.

Calculation:

In this, put $x=5$ in the expression,

  $\begin{array}{l}27x^2-30x-13\\ $ 27\cdot {(5)}^2-30\cdot 5-13$675-150-13\\ 512\end{array}$

Conclusion:

The area will be $512$ .