Chapter EP, Problem 6.6.15EP

To determine

To evaluate:

The value of the given number.

Answer to Problem 6.6.15EP

The value of given operation is $\left(x+\frac{5}{2}\right),\left(x-4\right)$ .

Explanation of Solution

Given:

The order of operation

  $2x^3-15x^2-2x+120$

Concept used:

Product means the answer to a multiplication problem

Sum means the total amount resulting from the addition of two or more numbers amounts or items

Quotient means a result obtained by dividing one quantity by another

Calculation:

The order of operation

The order of operation

  $=2x^3-15x^2-2x+\mathrm{120...................}\left(1\right)$

Putting $x=-\frac{5}{2},4$ in equation (1)

  $\begin{array}{l}f\left(x\right)=2x^3-15x^2-2x+120\\ f\left(-\frac{5}{2}\right)=2{\left(-\frac{5}{2}\right)}^3-15{\left(-\frac{5}{2}\right)}^2-2\left(-\frac{5}{2}\right)+120\\ f\left(-\frac{5}{2}\right)=2\left(-\frac{125}{8}\right)-15\left(\frac{25}{4}\right)+5+120\\ f\left(-\frac{5}{2}\right)=0\\ f\left(4\right)=2{\left(4\right)}^3-15{\left(4\right)}^2-2\left(4\right)+120\\ f\left(4\right)=2\left(64\right)-15\left(16\right)-8+120\\ f\left(4\right)=0\end{array}$

Therefore,

The value of given operation is $\left(x+\frac{5}{2}\right),\left(x-4\right)$