Chapter EP, Problem 6.3.20EP

To determine

To find:

The value of $-3p\left(4a\right)-p\left(a\right)$

Answer to Problem 6.3.20EP

The value of, $-3p\left(4a\right)-p\left(a\right)=\left[-102a^2-45a\right]$

Explanation of Solution

Given:

  $\begin{array}{l}p\left(x\right)=-2x^2+5x+1\\ m\left(x\right)=x^3-1\end{array}$

Concept:

Using the given value of the function

Calculation:

The function

  $p\left(x\right)=-2x^2+5x+\mathrm{1.........}\left(1\right)$

Putting the value $x=4a,a$ in equation (1)

  $\begin{array}{l}-3p\left(4a\right)-p\left(a\right)\\ p\left(x\right)=-2x^2+5x+1\\ -3p\left(4a\right)-p\left(a\right)=-3\left[-2{\left(4a\right)}^2+5\left(4a\right)+1+2a^2-5a-1\right]\\ -3p\left(4a\right)-p\left(a\right)=\left[-96a^2-60a-3-6a^2+15a+3\right]\\ -3p\left(4a\right)-p\left(a\right)=\left[-102a^2-45a\right]\end{array}$