Chapter 7: Q38. (page 351)

If $p (x) = 3 x^{2} - 2 x + 5 and r (x) = x^{3} + x + 1$ then find $3 [p (x^{2} - 1)] + 4 p (x)$ .

Short Answer

Expert verified

The value of $3 [p (x^{2} - 1)] + 4 [p (x)] = 9 x^{4} - 12 x^{2} - 8 x + 50$ .

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 $3 [p (x^{2} - 1)] + 4 p (x)$ by plugging $x = x^{2} - 1$ in given function $p (x) = 3 x^{2} - 2 x + 5$ and multiply it by 3 and then add $4 [p (x)]$ .

Therefore,

role="math" localid="1648124984708" $\begin{matrix} p (x) = 3 x^{2} - 2 x + 5 .... (Given) \\ 3 [p (x)] = 3 [3 x^{2} - 2 x + 5] \\ 3 [p (x^{2} - 1)] = 3 [3 {(x^{2} - 1)}^{2} - 2 (x^{2} - 1) + 5] \\ = 3 [3 x^{4} - 8 x^{2} + 10] \\ = 9 x^{4} - 24 x^{2} + 30 .... (1) \\ Now,4 [p (x)] = 4 [3 x^{2} - 2 x + 5] \\ = 12 x^{2} - 8 x + 20 .... (2) \end{matrix}$

Adding (1) and (2) gives,

$\begin{matrix} 3 [p (x^{2} - 1)] + 4 [p (x)] = 9 x^{4} - 24 x^{2} + 30 + 12 x^{2} - 8 x + 20 \\ = 9 x^{4} - 12 x^{2} - 8 x + 50 \end{matrix}$

Step 3. Conclusion.

The value of $3 [p (x^{2} - 1)] + 4 [p (x)] = 9 x^{4} - 12 x^{2} - 8 x + 50$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

If $p (x) = 3 x^{2} - 2 x + 5 and r (x) = x^{3} + x + 1$ then find $3 [p (x^{2} - 1)] + 4 p (x)$ .

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

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

If px=3x2-2x+5andrx=x3+x+1 then find 3px2-1+4px.

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

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

If $p (x) = 3 x^{2} - 2 x + 5 and r (x) = x^{3} + x + 1$ then find $3 [p (x^{2} - 1)] + 4 p (x)$ .