Question

If $p\left(x\right)=3x^2-2x+5\text{and}r\left(x\right)=x^3+x+1$ then find $4p\left(a\right)$.

Short answer

The value of $4p\left(a\right)=12a^2-8a+20$.

Step-by-step solution

Step 1. Write down the given information.

The given functions are $p\left(x\right)=3x^2-2x+5\text{and}r\left(x\right)=x^3+x+1$.

Step 2. Calculation.

Evaluating $4p\left(a\right)$ by plugging $x=a$ in given function $p\left(x\right)=3x^2-2x+5$ and multiply by 4.

$\begin{array}{c}p\left(x\right)=3x^2-2x+\mathrm{5....}\left(\text{Given}\right)\\ 4p\left(x\right)=4\left(3x^2-2x+5\right)\\ 4p\left(a\right)=4\left(3{\left(a\right)}^2-2\left(a\right)+5\right)\\ =12a^2-8a+20\end{array}$

Step 3. Conclusion.

The value of $4p\left(a\right)=12a^2-8a+20$.