# Use your results to write the complete factorization of f(x). Function f(x) = 2x^3 - x^2 - 10x + 5 Factors (2x - 1), (x + sqrt5)

Question
Functions
Use your results to write the complete factorization of f(x). Function $$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{3}}-{x}^{{2}}-{10}{x}+{5}$$ Factors $$\displaystyle{\left({2}{x}-{1}\right)},{\left({x}+\sqrt{{5}}\right)}$$

2020-10-21
Use part b to write the complete factorization.
$$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{3}}-{x}^{{2}}-{10}{x}+{5}$$
$$\displaystyle={\left({2}{x}-{1}\right)}{\left({x}+\sqrt{{5}}\right)}{\left({x}-\sqrt{-}{5}\right)}$$

### Relevant Questions

The graph of y = f(x) contains the point (0,2), $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{-{x}}}{{{y}{e}^{{{x}^{{2}}}}}}}$$, and f(x) is greater than 0 for all x, then f(x)=
A) $$\displaystyle{3}+{e}^{{-{x}^{{2}}}}$$
B) $$\displaystyle\sqrt{{{3}}}+{e}^{{-{x}}}$$
C) $$\displaystyle{1}+{e}^{{-{x}}}$$
D) $$\displaystyle\sqrt{{{3}+{e}^{{-{x}^{{2}}}}}}$$
E) $$\displaystyle\sqrt{{{3}+{e}^{{{x}^{{2}}}}}}$$

Use the piecewise-defined function to fill in the bla
.
$$\displaystyle{f{{\left({x}\right)}}}={\left\lbrace{4},-{4}{<}{x}{<}-{2},{2}{x}-{4},-{1}{<}{x}{<}{2},{3}{x},{2}\le{x}{<}{5}\right\rbrace}$$
a. The domain ____ is used when graphing the function $$f(x)=2x-4$$.
b. The equation ____ is used to find $$f(4)=12.$$

Use the theorems on derivatives to find the derivatives of the following function:
$$\displaystyle{f{{\left({x}\right)}}}={\left({5}{x}^{{{3}}}+{8}{x}^{{{2}}}-{4}\right)}^{{{4}}}{\left({8}{x}^{{{4}}}-{2}{x}^{{{3}}}-{7}\right)}$$
Find f'(a)
$$\displaystyle{f{{\left({t}\right)}}}={\frac{{{3}{t}+{3}}}{{{t}+{2}}}}$$
Suppose that f(x) is a continuous, one-to-one function such that $$\displaystyle{f{{\left({2}\right)}}}={1},{f}'{\left({2}\right)}=\frac{{1}}{{4}},{f{{\left({1}\right)}}}={3}$$, and f '(1) = 7. Let $$\displaystyle{g{{\left({x}\right)}}}={{f}^{{−{1}}}{\left({x}\right)}}$$ and let $$\displaystyle{G}{\left({x}\right)}={x}^{{2}}\cdot{g{{\left({x}\right)}}}$$. Find G'(1). (You may not need to use all of the provided information.)
Use the theorems on derivatives to find the derivatives of the following function:
$$\displaystyle{f{{\left({x}\right)}}}={3}{x}^{{{5}}}-{2}{x}^{{{4}}}-{5}{x}+{7}+{4}{x}^{{-{2}}}$$
A canyon is 900 meters deep at its deepest point. A rock is dropped from the rim above this point. Write the height of the rock as a function of time t in seconds. (Use -9.8 m/s2 as the acceleration due to gravity.) How long will it take the rock to hit the canyon floor? (Give your answer correct to 1 decimal place.)

Use exponential regression to find a function that models the data. $$\begin{array}{|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 \\ \hline f(x) & 14 & 7.1 & 3.4 & 1.8 & 0.8 \\ \hline \end{array}$$

$$a^m inH$$
$$f(x)= \begin{array}{11}{5}&\text{if}\ x \leq2 \ 2x-3& \text{if}\ x>2\end{array}$$
$$a^m inH$$
The function given by $$\displaystyle{f{{\left({x}\right)}}}=−{3}{x}^{{5}}+√{2}{x}+\frac{{1}}{{2}}{x}$$ (is/is not) a polynomial function.