Chapter 8.6, Problem 36PPE

To determine

To simplify:the length of table.

Answer to Problem 36PPE

The length of the rectangular table is $6x+15$ .

Explanation of Solution

Given information:

The area of rectangular table is $18x^2+69x+60$ . Width of the rectangular table is $3x+4$ .

Calculation:

Area of the rectangle is expressed as follows:

  $A=lb$

Here, l is length and b is width of rectangular table.

Factorize the polynomial as area of rectangular table as follows:

  $\begin{array}{c}A=18x^2+69x+60\\ =3\left(6x^2+23x+20\right)\\ =3\left(6x^2+15x+8x+20\right)\\ =3\left(3x\left(2x+5\right)+4\left(2x+5\right)\right)\\ lb=3\left(2x+5\right)\left(3x+4\right)\\ l\left(3x+4\right)=\left(6x+15\right)\left(3x+4\right)\\ l=\left(6x+15\right)\end{array}$

Thus, the length of the rectangular table is $6x+15$ .