MATH CLASS: EXPONENTS AND POLYNOMIALS (TUTOR DANIEL ONLY)

Case

Assignment Expectations

Simplify.

1.    (4²)³

2.   

3.   

4.    (a⁴b⁶)⁰

5.    (-2x)^-6

Evaluate each polynomial for the given value of the variable.

1. -x²-5x+6; x = -3

2. 2x²-4x-1; x = 5

   Add the polynomials.

1. (4y+5y²) + (2y³-8y²)

2. (3x²-2x-3) + (-7x²+5-8x)

   Subtract the polynomials.

1. (4a²+9b⁵) – (-2a²-6b⁵)

2. (-7-2z³+4y) – (3z³+12-6y)

   Use the FOIL method to simplify the binomials.

1. (x-10) (x-9)

2. (2x-2) (x+5)

3. (3y-4)²

4. 3x(x-1) (5x+9)

5. (y-3)(2y³-4y+5)

   Compute and write your answer in scientific notation.

1. (5.2 x 10¹³) (7.1 x 10^-22)

2. (4.3 x 10^-8) (1.5 x 10⁹)

3. 8.2 x 10⁵
   2.75 x 10^-3

4. 6.3 x 10^-7
   3.25 x 10^-12

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SLP

Write the final answer in the terms being asked such as dollars/cents, degrees, tickets, etc.

1.    Your friend Mary computes (x⁵)(x⁷) and gets and answer of x³⁵. Explain why her answer is incorrect and include the correct answer.

2.    Is (x+y)² equal to (x²+y²)? Explain why or why not using an example to support your answer.

3.    When multiplying two terms with the same base, _____________ the exponents. When dividing two terms with the same base, _____________ the exponents.

4.    John wants to hire an editor to check his thesis paper. The editor charges a flat rate of $50 and $2 per page. Write a polynomial to describe the cost. Find the cost of editing 75 pages.

5.    The distance from the Earth to the sun is 93,000,000 miles. Write this number in scientific notation.

6.    A scientist measures a speck of sand as having a diameter of 0.00000034. Write this number in scientific notation.

7.    Stacy wants to build a triangular sand box for her son. Using the figure below, calculate the area of the triangular box, writing the answer as a polynomial.

(Hint: A=1/2bh)

1. Victoria wants to plant a vegetable garden in the shape of a square. She has a space allocated in her backyard that will accommodate 175 square feet. Using the drawing below, use the FOIL method to find the polynomial that represents the area of the square. If x=6, will she have enough room to plant the garden?

   https://tlc.trident.edu/content/enforced/51134-MAT101-FEB2015-2/images/MAT101%20SLP%205_8.PNG?_&d2lSessionVal=dbaqTXHs6USYXVJyMEaXffHyA&ou=51134

1. Sam needs to fill up a box with packaging material. Use the picture below to calculate the volume of the box.

   https://tlc.trident.edu/content/enforced/51134-MAT101-FEB2015-2/images/MAT101%20SLP%205_9.PNG?_&d2lSessionVal=dbaqTXHs6USYXVJyMEaXffHyA&ou=51134

1. Jen and Jacob want to put a concrete deck around their pool. Use the figure below to calculate the area of the deck. Second, simplify the area if x=4.75. Round to the nearest hundredth.

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Laws of Exponents

What are three laws of exponents (for multiplication, division, and powers)? Write and explain each law. Why do we use exponents in scientific notation (you can provide an example)?

Write 2 problems containing exponents for your peers to simplify. Return to the discussion to check your peers’ understanding and offer help as needed. Be sure to post the answers at the close of the module