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Chapter 7: Q26. (page 350)

Find $p (4) and p (- 2)$ for the function $p (x) = x^{4} - 7 x^{3} + 8 x - 6$ .

Short Answer

Expert verified

The value of $p (4) = - 166 and p (- 2) = 50$ .

Step by step solution

01

Step 1. Write down the given information.

The given function is $p (x) = x^{4} - 7 x^{3} + 8 x - 6$ .

02

Step 2. Calculation.

Evaluating $p (4) and p (- 2)$ by plugging $x = 4 and x = - 2$ in given function $p (x) = x^{4} - 7 x^{3} + 8 x - 6$ .

$\begin{matrix} p (x) = x^{4} 鈭� 7 x^{3} + 8 x 鈭� 6 .... (Given) \\ p (4) = {(4)}^{4} 鈭� 7 {(4)}^{3} + 8 (4) 鈭� 6 \\ = 鈭� 166 \\ Now, p (鈭� 2) = {(鈭� 2)}^{4} 鈭� 7 {(鈭� 2)}^{3} + 8 (鈭� 2) 鈭� 6 \\ = 50 \end{matrix}$

03

Step 3. Conclusion.

The value of $p (4) = - 166 and p (- 2) = 50$ .

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Most popular questions from this chapter

The number of cable TV systems after 1985 can be modeled by the function $C (t) = - 43.2 t^{2} + 1343 t + 790$ , where (t) represents the number of years since 1985. What trends in cable TV subscriptions does the graph suggest ?

State the degree and leading coefficient of polynomial $2 b + 4 b^{3} - 3 b^{5} - 7$ in one variable. If it is not a polynomial in one variable, explain why.

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

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.

Graph each polynomial function. Estimate the x-coordinates at which the relative maxima and relative minima occur.

$鈥� f (x) = x^{3} + 2 x^{2} - 3 x - 5$

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