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Chapter 7: Q33. (page 351)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Write down the given information.

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

02

Step 2. Calculation.

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

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

03

Step 3. Conclusion.

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

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