Find a polynomial function $P(x)$ having leading coefficient one, least possible degree, real coefficients, and the given zeros.

$1+\sqrt{2}, 1-\sqrt{2}$, and $3$

Predict the end behavior of $P(x)=2x^3-9 x^2+4 x+15$

Solve the given equation. For equations with real solutions, support your answers graphically.

$$(4 x+1)^2=20$$

Give a short written answer in this exercises.

Repeat the previous exercise for $f(x)=x^n$, where $n=2,4,6, \ldots$.

A projectile is fired vertically upward, and its height in feet after $t$ seconds is given by

$$s(t)=-16 t^2+800 t+600 .$$

Graph this function in the window $[0,60]$ by $[-1000,11,000]$, and use either analytic or graphical methods to answer the exercise. From what height was the projectile fired?

Solve this equation analytically for all complex solutions, giving exact forms in your solution set. Then graph the left side of the equation as $\mathrm{Y}_1$ in the suggested viewing window and, using the capabilities of your calculator, support the real solutions.

$9 x^4+35 x^2-4=0$; $[-3,3]$ by $[-10,100]$

Give a short written answer in this exercises.

The graphs of $f(x)=x^n$ for $n=3,5,7, \ldots$ resemble each other. As $n$ gets larger, what happens to the graph?

Find a polynomial function $P(x)$ having leading coefficient one, least possible degree, real coefficients, and the given zeros.

$-3,2$, and $i$

Solve the given equation. For equations with real solutions, support your answers graphically.

$$(3 x-1)^2=12$$

Find the quotient when $P(x)$ is divided by the specified binomial.

$$P(x)=x^3+2 x^2-17 x-10 ;\quad x+5$$

A car travels a total of 275 miles in 4 hours, traveling part of the time at 60 miles per hour and part of the time at 74 miles per hour. How long did the car travel at each speed?

Solve this equation analytically for all complex solutions, giving exact forms in your solution set. Then graph the left side of the equation as $\mathrm{Y}_1$ in the suggested viewing window and, using the capabilities of your calculator, support the real solutions.

$x^4-15 x^2-16=0$; $[-5,5]$ by $[-100,100]$

Solve the given problem.

A piece of cardboard is twice as long as it is wide. It is to be made into a box with an open top by cutting two-inch squares from each corner and folding up the sides. Let $x$ represent the width of the original piece of cardboard.

(a) Represent the length of the original piece of cardboard in terms of $x$.

(b) What will be the dimensions of the bottom rectangular base of the box? Give the restrictions on $x$.

(c) Determine a function $V$ that represents the volume of the box in terms of $x$.

(d) For what dimensions of the bottom of the box will the volume be $320$ cubic inches? Determine analytically and support graphically.

(e) Determine graphically (to the nearest tenth of an inch) the values of $x$ if the box is to have a volume between $400$ and $500$ cubic inches.

Find a polynomial function $P(x)$ having leading coefficient one, least possible degree, real coefficients, and the given zeros.

$6$ and $-2$