Question

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

Short answer

The value of $p\left(x^2+3\right)=3x^4+16x^2+26$.

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

$\begin{array}{c}p\left(x\right)=3x^2-2x+5....\left(\text{Given}\right)\\ p\left(x^2+3\right)=3{\left(x^2+3\right)}^2-2\left(x^2+3\right)+5\\ =3\left(x^4+9+6x^2\right)-2x^2-6+5\\ =3x^4+16x^2+26\end{array}$

Step 3. Conclusion.

The value of $p\left(x^2+3\right)=3x^4+16x^2+26$.