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Chapter 7: Q8. (page 350)

Find $p (3) and p (- 1)$ for the function $p (x) = x^{4} - 3 x^{3} + 2 x^{2} - 5 x + 1$ .

Short Answer

Expert verified

The value of $p (3) = 4 and p (- 1) = 12$ .

Step by step solution

01

Step 1. Write down the given information.

The given function is $p (x) = x^{4} - 3 x^{3} + 2 x^{2} - 5 x + 1$ .

02

Step 2. Calculation.

Evaluating $p (3) and p (- 1)$ by plugging $x = 3 and x = - 1$ in given function $p (x) = x^{4} - 3 x^{3} + 2 x^{2} - 5 x + 1$ .

$\begin{matrix} p (x) = x^{4} 鈭� 3 x^{3} + 2 x^{2} 鈭� 5 x + 1.... (Given) \\ p (3) = {(3)}^{4} 鈭� 3 {(3)}^{3} + 2 {(3)}^{2} 鈭� 5 (3) + 1 \\ = 4 \\ Now, p (鈭� 1) = {(鈭� 1)}^{4} 鈭� 3 {(鈭� 1)}^{3} + 2 {(鈭� 1)}^{2} 鈭� 5 (鈭� 1) + 1 \\ = 12 \end{matrix}$

03

Step 3. Conclusion.

The value of $p (3) = 4 and p (- 1) = 12$ .

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Most popular questions from this chapter

For each graph,

a. Describe the end behaviour.

b. Determine whether it represents an odd-degree or an even-degree polynomial function, and

c. state the number of real zeros.

Complete each of the following.

Graph each function by making a table of values.
Determine consecutive values of x between which each real zero is located.
Estimate the x-coordinate at which the relative maxima and relative minima occur.

$f (x) = x^{5} - 6 x^{4} + 4 x^{3} + 17 x^{2} - 5 x - 6$

Find $p (4) and p (- 2)$ for the function $p (x) = \frac{1}{8} x^{3} - \frac{1}{4} x^{2} - \frac{1}{2} x + 5$ .

Complete each of the following.

Graph each function by making a table of values.
Determine consecutive values of x between which each real zero is located.
Estimate the x-coordinate at which the relative maxima and relative minima occur.

f (x) = x^{3} - 2 x^{2} + 6

Graph the polynomial function $f (x) = x^{4} - 7 x^{2} + x + 5$ by making table of values.

See all solutions

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