8th Grade Math Unit 9

8th Grade Math Unit 9 - Factoring

Which is the correct factorization of this monomial:

-90x³yz²

Review Factoring
1. 2 • 3 • 3 • 5 • x • x • x • y • z • z
2. - 1 • 2 • 3 • 3 • 5 • x • x • y • z • z
3. - 1 • 2 • 3 • 3 • 5 • x • x • x • y • z • z
4. - 1 • 2 • 3 • 3 • 5 • x • x • x • y • y • z • z
Check the statements below that are correct.
(Check all that apply.)
1. The prime factorization of - 150 is:
  -1, 2, 3, 5, 5,
2. The factors of - 144 a³bc² are:
  - 2 • 2 • 2 • 2 • 3 • 3 • a • a • b • c • c
3. The prime factors of 360 are:
  2 • 2 • 2 • 3 • 3 • 5
4. The factors of 246x⁴y are:
  
  2 • 3 • 41
5. The factors of 121a³b²c³ are:
  
  11 • 11 • a • a • a • b • c • c • c
Check the statements below that are correct.
(Check all that apply.)

Review Factoring Polynomials
1. The GCF (Greatest Common Factor) of 21xy, 49y³ is: 7y
2. The GCF of 16x²y, 80x²y²z is: 16xy
3. The GCF of 18n², 30m²n is: 6mn
4. The GCF of 21a²b, 38c²d is: 38abcd
5. The GCF of 28x², 42x³y²,98y⁴ is: 14x
The formula (2^p - 1), where p is a prime number, will always result in another prime number for any valus of p.
1. True
2. False
Check the correct statements below:
(Check all that apply.)

Review Factoring
1. The factors of:
  12x² + 14x +6x + 7
  are: (2x + 1) (6x + 1)
2. The factors of:
  12x²y²z + 48 xy³z² are:
  12xy²z(x + 4yz)
3. The factors of:
  12a² - 30a - 2a + 5 are:
  (6a - 1) (2a - 5)
4. The factors of:
  16x² - 14x - 24x + 21 are:
  (2x - 3) (8x - 7)
In the following figure, the length of the inside rectangle is a, and the width is b. If the length of the outside rectangle is 4 more than the length of the inside rectangle, and the width of the outside rectangle is 4 more than the width of the inside rectangle, what is the factored form of the area of the shaded portion.
1. 4a + 4b + 16
2. a² + 8a + 16
3. 4(a + b + 4)
4. 2(ab +2a + 2b + 8)
Check the correct solutions below.
(Check all that apply.)
1. (2b - 5) (5b - 8) = 0
  b = { 5/2, 8/5 }
2. 9x² - 45x = 0
  x = { 5 }
3. 25a² = - 10a
  a = { 0, - 2/5 }
The factors of:
m^{x + y} + m^xn^y - m^yn^x - n^{x + y}
are:
1. (m^y - n^y)(m^x + n^x)
2. (m^x - n^x(m^y + n^y)
Which is the correct factorization of this monomial:

-90x³yz²

Review Factoring Polynomials
1. 2 • 3 • 3 • 5 • x • x • x • y • z • z
2. - 1 • 2 • 3 • 3 • 5 • x • x • y • z • z
3. - 1 • 2 • 3 • 3 • 5 • x • x • x • y • z • z
4. - 1 • 2 • 3 • 3 • 5 • x • x • x • y • y • z • z
The total number of feet in a yards, b feet, and c inches is:
1. 3(a + b + c /12)
2. (a + b + c)/12
3. 3a + b + c /12
4. 3a + b + 12c
The factors of this trinomial are:

- 42 + 11x + x²

Review Factoring Trinomials
1. (x + 7) (x - 6)
2. (x + 14) (x - 3)
3. (x - 14) (x + 3)
4. (x - 7) (x + 6)
Check all the solutions below that are correct
1. A rectangle has an area of:
  x² + 7x - 60
  The perimeter of this rectangle is:
  4x + 14
2. a² + 30 = - 13a
  a = {10, 3}
3. x² - x + 64 = - 21x
  x = {- 16, - 4)
The area of a right triangle is 24 sq. ft.
What is the height (h) of this triangle if the base is (2h + 10)
h = ________ ft.
The factors of:
x² - 17x + 42 are:
1. (x + 3)(x + 14)
2. (x - 3)(x + 14)
3. (x - 7)(x - 6)
4. (x - 3)(x - 14)
Check the trinomials that have the correct factors below:

Review Factoring Trinomials
1. 3a² + 5a + 2
  (3a + 2)(a + 1)
2. 9x² + 24xy + 16y²
  (3x + 4y)(3x - 4y)
3. 36x² - 24xy - 5y²
  (6x + y)(6x - 5y)
Check the equations below that have the correct solutions:
1. (3y + 2)(y + 4) = - 2y + 20
  y = { -2/3, 6}
2. x²/12 - 5x/3 - 8 = 0
  x = { - 24, 4 }
3. 5x² + 28x + 15 = 0
  x = { - 25, - 3 }
The solutions of 4a² - 2a - 6 = 0 are:
1. 2/3 and 1
2. 3/2 and 1
3. 3/2 and - 1
4. 2/3 and - 1
n² - 35 is prime.
1. True
2. False
Check the polynomials below that have the correct factors or are labled "prime":
1. - 25 + 64x²
  (8x + 5) (8x + 5)
2. 144a² - b²
  (12a + b) (12a - b)
3. - 9x² + 113
  Prime
4. 18b⁴ - 72b²
  18(b + 2)(b - 2)
5. x³ + 5x² - 9x - 45
  (x + 3) (x - 3) (x + 5)
Check the correct solutions to the equations below:
1. x² - 9/64 = 0
  x = 3/8 and - 3/8
2. 49 - r²/16 = 0
  r = 7 and -7
3. 27b³ - 192b = 0
  b = 0 and 8/3 and - 8/3
4. -16 x³ + 36x = - 4x⁴ + 9x²
  x = {0, 3/2, - 3/2 }
The factors of:
(1/2) am² - (1/2) an²
are:
1. (a/2) (m + n)²
2. (a/2) (m - n)²
3. (a/2) (m + n) (m - n)
4. (1/2) (m + n) (m - n)
What three conditions must be satisfied for a trinomial to be factorable as a perfect square?
1. The last term must be a perfect square
2. The middle term must be the product of the square roots of the first and last terms.
3. The fist term must be a perfect square.
4. The middle term must be twice the product of the square roots of the first and last terms.
Check the trinomials below that are perfect squares.
1. y² + 8y + 64
2. m² + 22m + 121
3. 25x² - 120 x + 144
4. 2 y² + 10 y + 25
Which polynomial below is prime?
1. 20x² + 34 x + 6
2. y² + 6y - 9
3. m² - 36
4. 8a³ + 6a²b² +18a +12b²
Solve for m:
m² + (4/5)m + 4/25 = 0

m = __________
1. 2 1/2
2. - (2/5)
3. 5
4. 2