Question

If $p\left(x\right)=2x^3+6x-12\text{and}q\left(x\right)=5x^2+4$ then find $p\left(a^3\right)$.

Short answer

The value of $p\left(a^3\right)=2a^9+6a^3-12$.

Step-by-step solution

Step 1. Write down the given information.

The given functions are $p\left(x\right)=2x^3+6x-12\text{and}q\left(x\right)=5x^2+4$.

Step 2. Calculation.

Evaluating $p\left(a^3\right)$ by plugging $x=a^3$ in given function $p\left(x\right)=2x^3+6x-12$.

$\begin{array}{c}p\left(x\right)=2x^3+6x-\mathrm{12....}\left(\text{Given}\right)\\ p\left(a^3\right)=2{\left(a^3\right)}^3+6\left(a^3\right)-12\\ =2a^9+6a^3-12\end{array}$

Step 3. Conclusion.

The value of $p\left(a^3\right)=2a^9+6a^3-12$.