Use the Factor Theorem to show that the statement in the exercise is true. Show that x + 4 is a factor of the polynomial $P(x)=x^{5}+4 x^{4}-7 x^{3}-23 x^{2}+23 x+12$

Answer the exercise given below.

Use the Factor Theorem to show that x+4 is a factor of the polynomial

$$P(x)=x^5+4 x^4-7 x^3-23 x^2+23 x+12$$

confirm your results by using a graphing utility to graph the function. Function

$$f(x) = x^3 + 3x^2 - 48x - 144$$

Factors

$$(x+4√3), (x + 3)$$

Translate the equation into a sentence. 7(p + 23) = 102

Factor the expression completely. $\frac{4(2 x+3)^{2}-(4 x-1)(2)(2 x+3)(2)}{(2 x+3)^{4}}$

Random products mod 10. Pick two successive digits from a table of random digits from $\{0,1, \ldots, 9\}$. Multiply them together, and let $D$ be the last digit of this random product. For example,

$$\begin{gathered} (3,9) \rightarrow 27 \rightarrow 7 \\ (2,4) \rightarrow 8 \rightarrow 8 \end{gathered}$$

Find the distribution of $D$, and calculate its mean.

A chilled orange juice warehousing operation in New York City was experiencing too many out-of-stock situations with its 96-ounce containers. To better understand current and future demand for this product, the company examined the last 40 days of sales, shown in the table below. One of the company's objectives is to model demand, $y$, as a function of sale day, $x$ (where $x=1,2,3, \ldots, 40)$.

b. Does a second-order model appear to explain the variation in demand better than a first-order model? Justify.

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. $R(x)=\frac{8 x^{2}+26 x-7}{4 x-1}$

On each line, complete the word group with a correct singular or plural word. Write S after a singular word and P after a plural word.

Example 1. those breathtaking $\underline{\text{photographs P}}$

a few more_______________

Solve the linear system by using elimination.

$$\begin{array}{l} x+5 y=28 \\ -x-2 y=-13 \end{array}$$

Solve each problem using an appropriate method. In how many ways can the digits in the number 335,557 be arranged?

Find each sum.

$$-51+23=$$

Calculate the mean absolute deviation. Round your answers to 3 significant digits when you can.

$$43.4,30.5,20.0,23.6,34.5,36.9,11.7,40.2$$

The percent by mass of bicarbonate $(\mathrm{HCO_3^-})$ in a certain Alka-Seltzer product is 32.5 percent. Calculate the volume of $\mathrm{CO_2}$ generated (in mL) at 37 °C and 1.00 atm when a person ingests a 3.29-g tablet. (Hint: The reaction is between $\mathrm{HCO_3^-}$ and HCl acid in the stomach.)