Question

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

Short answer

The value of $5\left[q\left(2a\right)\right]=100a^2+20$.

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 $5\left[q\left(2a\right)\right]$ by plugging $x=2a$ in given function $q\left(x\right)=5x^2+4$and multiply by 5.

$\begin{array}{c}q\left(x\right)=5x^2+\mathrm{4....}\left(\text{Given}\right)\\ 5\left[q\left(x\right)\right]=5\left[5x^2+4\right]\\ 5\left[q\left(2a\right)\right]=5\left[5{\left(2a\right)}^2+4\right]\\ =100a^2+20\end{array}$

Step 3. Conclusion.

The value of $5\left[q\left(2a\right)\right]=100a^2+20$.