Chapter 7: Q37. (page 351)

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

Short Answer

Expert verified

The value of $r (x + 1) - r (x^{2}) = - x^{6} + x^{3} + 2 x^{2} + 4 x + 2$ .

Step by step solution

Step 1. Write down the given information.

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

Step 2. Calculation.

Evaluating $r (x + 1) - r (x^{2})$ by plugging $x = x + 1 and x = x^{2}$ in given function $r (x) = x^{3} + x + 1$ and then subtracting $r (x^{2})$ from $r (x + 1)$ .

Therefore,

$\begin{matrix} r (x) = x^{3} + x + 1 .... (Given) \\ r (x + 1) = {(x + 1)}^{3} + (x + 1) + 1 \\ = x^{3} + 1 + 3 x^{2} + 3 x + x + 1 + 1 \\ = x^{3} + 3 x^{2} + 4 x + 3.... (1) \\ Now, r (x^{2}) = {(x^{2})}^{3} + (x^{2}) + 1 \\ = x^{6} + x^{2} + 1.... (2) \end{matrix}$

Subtracting (2) from (1) gives,

$\begin{matrix} r (x + 1) - r (x^{2}) = (x^{3} + 3 x^{2} + 4 x + 3) - (x^{6} + x^{2} + 1) \\ = - x^{6} + x^{3} + 2 x^{2} + 4 x + 2 \end{matrix}$

Step 3. Conclusion.

The value of $r (x + 1) - r (x^{2}) = - x^{6} + x^{3} + 2 x^{2} + 4 x + 2$ .

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

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

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If px=3x2-2x+5andrx=x3+x+1 then find rx+1-rx2.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

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