8th Grade Math Unit 8 - Add, Subtract, Multiply Polynomials

Check which expressions below are monomials.

(Check all that apply.)

Review Products and Quotients of Monomials
1. 3y³
2. 2a + 5b
3. m/n²
4. (1/5)xyz⁴
5. 5y³
Which expression below results from simplifying:

(12ab⁵c⁴)(4a⁴b⁷c³
1. 12a⁵b¹²c⁷
2. 48a⁴b¹²c¹²
3. 48a⁴b³⁵c¹²
4. 48a⁵b¹²c⁷
Simplify:

(5xy)³( - 2y²)³ = -1000x³y⁹
1. True
2. False
Simplify and check the correct answer below:

(5a/7)²(42a)(18b)(b⁶/36)
1. (325/7)a³b⁷
2. (75/7)a³b⁷
3. (325/7)a²b⁷
4. (325/7)a³b⁶
Which monomial below represents the area of the following figure:
1. 4x⁴y⁴
2. 16x³y²
3. 16x⁴y⁴
4. 16x³y⁴
Which monomial below expresses the volume of the following figure:

( π = pi )
1. 25 π a⁶ b⁴
2. 150 π a⁶ b⁴
3. 150 π a³ b⁴
4. 30 π a⁶ b⁴
For all real numbers x and y, and all integers n,
(x + y)ⁿ = xⁿ + yⁿ

Hint: Try substituting some numbers for x, y and n.
1. True
2. False
Which of the following simplifications are correct, assuming no denominator equals zero.

(Check all that apply)

π = pi
1. [(πr²)(2r)]/(4/3)πr³ = 3/2
2. (3/5)^-2 = 9/25
3. (14a³b⁴c⁹)/(-2a²bc = -7ab³c⁸
4. (35x⁷z^-5)/(7x⁵y⁰z^-7 = 5x²z¹²
5. [ (3a^-2bc^-1)/(4ab^-2 ]^-3 = 64/(27a^-9b⁹c^-3)
If the area of a right triangle is 100x³, and its base is 25x², what is its height?
If you simplify:

5a^{3x - 9}/ a^{4(x - 5)}

you get:
1. 5a^{x + 29}
2. 5a^{- x - 11}
3. 5a^{- x - +11}
4. 5a^{4x + 20}
Check the statements below that are correct.

Check all that apply.

Review Scientific Notation
1. 8.7 x 10^{- 6} = 0.0000087
2. 0.0000000435 = 4.35 x 10⁶
3. 4.782 x 10¹² = 4,782,000,000,000
4. 4.589 x 10⁰ = 4.589
5. 5.34 x 10^{- 5} = 0.0000534
Check the statements below that are correct.

Checl all that apply.
1. 24,504,000 = 2.4504 x 10⁷
2. 0.00087402 = 87402 x 10⁸
3. 0.000509 = 5.09 x 10^{- 4}
4. 490.75 = 4.9075 x 10²
Evaluate and express the result in standard notation:

(4.5 x 10⁸) (6.2 x 10^{- 5})
Express the following in scientific notation:

(3.2 x 10^{- 3})(8.4 x 10⁷ =
1. 26.88 x 10⁵
2. 2.688 x 10¹⁰
3. 2.688 x 10⁵
4. 2.688 x 10⁴
Express the following in scientific notation:

(3.816 x 10^{- 7})/(1.908 x 10⁶)
1. 2 x 10¹³
2. 2 x 10^{- 1}
3. 2 x 10^{- 13}
4. 2 x 10¹
A baseball player is paid $ 30 million per year. A teacher is paid $40 thousand per year. In scientific notation, how many times as great is a baseball player's salary as a teacher's salary?
1. 7.5 x 10³
2. 7.5 x 10²
3. 75 x 10²
4. 7.5 x 10⁴
If a country has a debt of $6.9644 trillion, and its population is 302.8 million people, how much is owed by each person in the country?

$ __________
1. 2.3 x 10³
2. 2.3 x 10⁴
3. 2.3 x 10⁵
4. 2.3 x 10⁶
Which of the following are equivalent to 658 x 10^{- 8}?

(Check all that apply.)
1. 0.0000658
2. 0.0000000068
3. 0.00000658
4. 6.58 x 10^{- 6}
Check the statements below that are correct.

(Check all that apply.)
1. (5a³/b) + a² is a polynomial.
2. (5m²/n³ + n² is a polynomial
3. - 2 + 3x + 7x³ is a polynomial
4. 278 is not a polynomial
What is the degree of the following polynomial?

8x⁴y² - 7x⁹y³
Which polynomial below is the result of arranging the following polynomial so that the powers of x are in ascending order.

8 x³y⁴ - 4y + 3x⁷y³ + 5x - 9
1. 3x⁷y³ + 8 x³y⁴ + 5x - 4y - 9
2. -9 -4y + 5x + 8 x³y⁴ + 3x⁷y³
3. 8x³y⁴ + 3x⁷y³ + 5x - 4y - 9
4. -9 -4y + 5x + + 3x⁷y³ + 8x³y⁴
Is polynomial below the result of arranging the following polynomial so that the powers of y are in decending order.

6x³y + 9xy⁴ - 3x²y³ + y⁴ =

(9x+1)y⁴ - 3x²y³ + 6x³y
1. Yes
2. No
You have a cylinder and a sphere that have the same radius. You cut the sphere in half and place the half on top of your cylinder to form a sculpture. If the radius of the cylinder and the sphere is 3 inches, and the height of the cylinder is 5 inches, what is the volume of your sculpture. Remember,

the volume of a cylinder is: π x the square of the radius x the height

The volume of a sphere is (4/3) x π x the cube of the radius

π is pi

It looks like this:
1. 36 π
2. 45 π
3. 81 π
4. 63 π
( - 4x³ - x +10) - (4x³ +3x² - 7) = ___________

Review Add, Subtract, and Multiply Polynomials
1. 2x + 3
2. -8x³ -4x +17
3. 8x³ -4x +17
4. -8x³ + 4x + 3
(4a + 3b - 6c) + (5b - 8a + 7c) - ( - 4c - 9a - 2b) = ____________
1. - 5a - 10b + 5c
2. 21a +10b +17c
3. 13a + 10b - 5c
4. 5a + 10b + 5c
(4x² + 3b² - 6x) - (3x² - 4bx - 8x) = ___________
1. x² + 3b² +4bx + 2x
2. x² + 3b² + 2x
3. 7x² + 3b² +4bx + 14x
4. x² + 3b² +4bx - 14x
(8x³ + 3x - 12) - (5x² - 4x) + (3x³ - x² - 8x + 6) = ___________
1. 5x³ - 6x² - x - 6
2. 11x³ + 6x² - x - 6
3. 11x³ - 6x² - x - 6
4. 5x³ - 6x² - x - 18
The perimeter of this triangle is:

P = 8x² - 7x + 12

What is the length of the third side?
1. 10x² - 15x + 10
2. 6x² - 15x + 10
3. 6x² - 1x + 10
4. 6x² + 1x + 18
The perimeter of this rectangle is 12a + 4b. Which expression below represents the length of the rectangle?
1. 2a + 4b
2. 20a + 8b
3. 4a + 8b
4. 4a + 4b
If x² - 3 xy + y² = x² - 5 xy + y², find xy.

xy = _______
Check The products that are correct below:
(Check all that apply.)
1. (- 2/3)mn²(3n² +6m - 9) = 2mn⁴ - 4m²n² + 6 mn²
2. 4a³b(3b + 6ab - b² + a³) = 4a⁹b + 24a⁴b - 4a³b³ + 12a³b²
3. 5p³q²(2p² - 2q² +7p³ +3q) = 7p⁶ + 2p⁵q² - 2p³q⁴ +3p³q³
If you simplify:

6a(2b³ - a² +9b³ + 3a)

you get:

- 6 a³ + 18a² + 66 ab³
1. True
2. False
Simplify:

3x²(x + 2) + 3x(5x² + 3x -7) - 4(2x² - 5x)

What is the coefficient in the term that contains x²
Find the area of the shaded region of the figure below:
1. 30a² - 12a
2. 12a² - 12a
3. 18a² - 12a
4. 18a² + 12a
Check which solutions are correct below:
1. 3x(x - 5) - 2x (x - 6) = x(x + 5) - 24
  x = 3
2. m(m - 6) + 13 = 2m + m(m + 5)
  
  m = 2
You go to the store to buy a new baseball bat which is being sold at 25% off the retail price. In addition, the store is giving your team another discount of n percent off the already discounted price. Which expression below will give the final cost if the retail price is p?
1. 0.25p(1 - n)
2. (p - 0.25p)(1 - n)
3. (p - 0.25p)(1 + n)
4. p(1 - 0.25 - n)
Simplify:

[ (2x² - 2x + 4) - (x² +6x -3)](x + 2)

The correct answer is: x³ - 6x² - 9x + 14
1. True
2. False
You charge your neighbor $25 for the first 30 minutes that you take care of their dog, and $3 for each additional minute that you care for their dog. If the neighbor paid you $76 for the job, how many minutes did you take care of their dog?

_________ minutes
Check which products below are correct.
(Check all that apply.)
1. (9a - 5b)(3a + 2b) = 27a² - 3ab + 10b²
2. (2x - 7)(3x² - 5x + 2) = 6x³ - 31x² +39x -14
3. (7x² - 4x + 3)(3x² + 2x - 4) = 21x⁴ + 2x³ - 27x² - 10x - 12
Which two expressions below represent the area of the following figure:
1. (2x - 2)(5x - 7) + 1/2[(x + 6) - (2x - 2)](5x - 7)
2. (x + 6)(5x - 7)
3. 1/2(x + 6)(5x + 7) + (2x -2)(5x - 7)
4. (5x -7) + (2x - 2) + (x + 6)
5. (1/2)[(x + 6) + (2x - 2)](5x - 7)
Your Dad is putting in a flower garden in the back yard. He wants its length to be 5 feet longer than the width. He will also be installling a brick walkway that is 3 feet wide around the flower garden. If he can only afford 426 square feet of brick, how wide should the flower garden be?

_______ feet
The expression (x - y)(x² + xy + y² is equivalent to which of the following?
1. x³ + 2x²y - y³
2. x³ + 2x²y - 2xy² - y³
3. x³ + y³
4. x³ - y³
Which of the following products are correct?
(Check all that are correct.)
1. (x + 6y)² = x² +6xy + 36y²
2. (7a² - 8b²)(7a² + 8b²) = 64a⁴ - 81b⁶
3. (m + 4)(m - 3)(m - 2)(m + 3) = m⁴ - 25m² + 144
4. (a - b)(a + b) = a² + b²
If (x + a)(x - b) is a binomial, then

Review Add, Subtract, and Multiply Polynomials
1. a = b
2. a > b
3. a < b
(x + a)(x - a) = x² - a²
1. True
2. False