Q32. - Algebra 2

Question

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

Step-by-Step Solution

Answer

The value of $p\left(a^2\right)=3a^4-2a^2+5$.

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

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

Step 3. Conclusion.

The value of $p\left(a^2\right)=3a^4-2a^2+5$.