Chapter EP, Problem 6.6.18EP

To determine

To evaluate:

The value of the given number.

Answer to Problem 6.6.18EP

The value of given operation is $\left(x+3\right),\left(x+5\right)$ .

Explanation of Solution

Given:

The order of operation

  $x^3+9x^2+23x+15$

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

  $=x^3+9x^2+23x+\mathrm{15...................}\left(1\right)$

Putting $x=-5,-3$ in equation (1)

  $\begin{array}{l}f\left(x\right)=x^3+9x^2+23x+15\\ f\left(-3\right)={\left(-3\right)}^3+9{\left(-3\right)}^2+23\left(-3\right)+15\\ f\left(-3\right)=-27+81-69+15\\ f\left(-3\right)=-96+96\\ f\left(-3\right)=0\\ f\left(-5\right)={\left(-5\right)}^3+9{\left(-5\right)}^2+23\left(-5\right)+15\\ f\left(-5\right)=-125+225-115+15\\ f\left(-5\right)=0\end{array}$

Therefore,

The value of given operation is $\left(x+3\right),\left(x+5\right)$ .