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Chapter 7: Q35. (page 351)

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

Short Answer

Expert verified

The value of $p (x^{2} + 3) = 3 x^{4} + 16 x^{2} + 26$ .

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

$\begin{matrix} p (x) = 3 x^{2} 鈭� 2 x + 5 .... (Given) \\ p (x^{2} + 3) = 3 {(x^{2} + 3)}^{2} 鈭� 2 (x^{2} + 3) + 5 \\ = 3 (x^{4} + 9 + 6 x^{2}) 鈭� 2 x^{2} 鈭� 6 + 5 \\ = 3 x^{4} + 16 x^{2} + 26 \end{matrix}$

03

Step 3. Conclusion.

The value of $p (x^{2} + 3) = 3 x^{4} + 16 x^{2} + 26$ .

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