Question

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

Short answer

The value of $2\left[p\left(x+4\right)\right]=6x^2+44x+90$.

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

$\begin{array}{c}p\left(x\right)=3x^2-2x+5....\left(\text{Given}\right)\\ 2p\left(x\right)=2\left(3x^2-2x+5\right)\\ 2\left[p\left(x+4\right)\right]=2\left[3{\left(x+4\right)}^2-2\left(x+4\right)+5\right]\\ =2\left[3x^2+48+24x-2x-8+5\right]\\ =6x^2+44x+90\end{array}$

Step 3. Conclusion.

The value of $2\left[p\left(x+4\right)\right]=6x^2+44x+90$.