Q33.

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

Verified

Answer

The value of $p (2 a^{3}) = 12 a^{6} - 4 a^{3} + 5$ .

1Step 1. Write down the given information.

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

2Step 2. Calculation.

Evaluating $p (2 a^{3})$ by plugging $x = 2 a^{3}$ in given function $p (x) = 3 x^{2} - 2 x + 5$ .

$\begin{matrix} p (x) = 3 x^{2} - 2 x + 5.... (Given) \\ p (2 a^{3}) = 3 {(2 a^{3})}^{2} - 2 (2 a^{3}) + 5 \\ = 12 a^{6} - 4 a^{3} + 5 \end{matrix}$

3Step 3. Conclusion.

The value of $p (2 a^{3}) = 12 a^{6} - 4 a^{3} + 5$ .