University:
Glendale Community College
Course:
MAT092 | Beggining Algebra
Academic year:

2020
Views:

422

Pages:

3
Author:

Ean Kidd

MAT 092 Beginning Algebra Test #8 NAME: KEY 1. State whether the following statements are TRUE or FALSE. No explanation is necessary. A) The binomial (x^{3}-27) is an example of the difference of cubes. FALSE B) The expression ((x+2)^{3}) is an example of the sum of cubes (x^{3}+27). FALSE C) (A^{3}-B^{3}=(A-B)(A^{2}+AB+B^{2})). TRUE 2. Create ONE polynomial that could be called the "DIFFERENCE OF SQUARES". LOTS of EXAMPLES (X^{2}-4) 3. Create ONE polynomial that could be called the "SUM OF CUBES". LOTS of EXAMPLES (x^{3}+8) 4. Draw a rectangular shape that would represent the given polynomial multiplication: ((2x+3)(x+4)) [Diagram of a rectangular shape representing polynomial multiplication] 5. Find a polynomial that would model the area of the following: [Diagram of a triangle with base x+3 and height 4x-1] A = (1/2)BH A = (1/2)(x+3)(4x-1) A = (1/2)(4x² + 11x - 3) A = 2x² + (11/2)x - (3/2) 6. Find the polynomial that would model the area of the shaded region: [Diagram of a rectangle with dimensions 10 and 20, with a smaller rectangle removed] A = LARGE - SMALL A = (10)(20) - (10-2x)(20-2x) A = 200 - (200 - 60x + 4x²) A = 60x - 4x² 7. Factor the following polynomial by using the GCF: A) 15x² - 21x GCF: 3x 3x(5x - 7) B) -12x³y³ + 10x²y² - 2xy² GCF: -2xy² -2xy²(6x²y - 5x + 1) 8. Factor the following polynomial by GROUPING: A) x³ - 3x² + 5x - 15 (x³ - 3x²) + (5x - 15) x²(x - 3) + 5(x - 3) (x - 3)(x² + 5) B) ax - bx - ay + by (ax - bx) - (ay - by) x(a - b) - y(a - b) (x - y)(a - b) 9. Factor the following polynomials using the AC Method or Guess-N-Check. You get to choose! A) x² - 4x - 45 AC = -18 (x - 9)(x + 5) B) 3x² - 7x - 6 AC = -18 3x² - 9x + 2x - 6 (3x² - 9x) + (2x - 6) 3x(x - 3) + 2(x - 3) (x - 3)(3x + 2) 10. Use a PATTERN to help you factor the following: A) 25x² - 9y² DIFF of SQUARES (5x)² - (3y)² (5x - 3y)(5x + 3y) B) 27x³ - 8 DIFF of CUBES (3x)³ - (2)³ (3x - 2)(9x² + 6x + 4) 11. "Put it all together": Factor the following polynomials completely. A) 12x³ - 18x GCF: 6x 6x(2x² - 3) B) 3x³ + 6x² - 24x GCF: 3x 3x(x² + 2x - 8) G-N-C: 3x(x + 4)(x - 2) C) x³ + 64 Sum of Cubes (x + 4)(x² - 4x + 16) D) 2x² - 3xy - 9y² G-N-C: (2x + 3y)(x - 3y)