Given: [7 points] Show work in your upload submission. Do not forget to show your long division process clearly and thoroughly. Input your answers in the provided space below. [1 pt] The maximum number of real zero is [a]. [1 pt] According to the Descartes’s Rule, the number of positive real zero is [b]. [1 pt] According to the Descartes’s Rule, the number of negative real zero is [c]. [2 pts] By the Rational Zeros Theorem, the possible rational zeros (in ascending order) are

Solve the given inequality by using the sign chart that we went over in our class’s lecture video. Write your answer in interval notation and graph the solution set. [5 pts] Show sign chart in your upload submission. [1 pt] Graph the solution set in your upload submission. Input your answers in the provided space below. [2 pts] The solution in interval notation is  (Use “inf” for “

Find the vertical, horizontal, oblique asymptote, and the hole of the given function, if any.  If there is not any, type ‘none.’ [3 pts] Show work in your upload submission. [1 pt] The vertical asymptote(s) is [a]. [1 pt] The horizontal asymptote(s) is [b]. [1 pt] The oblique asymptote(s) is [c]. [1 pt] The hole is at [d]. [3 pts] The domain in interval notation is [e] (Use “inf” for “

Solve: [5 pts] Show work in your upload submission. [1 pt] Solution(s): 

Use the Remainder Theorem and synthetic division to find the remainder when f(x) is divided by . Then use the Factor Theorem to determine whether  is a factor of f(x). [2 points] Show work in your upload submission. [2 points] By Remainder Theorem, [a]. [2 points] By Factor Theorem, [b].

Graph by analyzing the rational function. [3 pts] Graph in your upload submission. Input your answers in the given space below. [1 pt] The x-intercept(s) is ________ [1 pt] The y-intercept is ________ [1 pt] The vertical asymptote is (if any)________ [1 pt] The horizontal/oblique asymptote is (if any)________ [1 pt] The hole is at (if any)________ [2 pts] Give at least 3 additional points that are not from any of the above.

Use the definition of logarithm to find x. Give the exact solution and the approximated solution rounded to 3 decimal places. [4 points] Show work in your upload submission. [1 point] Exact solution: [a] [1 point] Approximated solution: [b]      (Round to 3 decimal places)  

How many bike are in the picture?

Look at those black clouds! It ______ soon.

After she ______ dinner, she will wash the dishes.