1 Answer each of the questions below 1 pt each a Write the n

1. Answer each of the questions below: (1 pt. each)

a) Write the number in scientific notation: 360,559,112

b) Write the number in scientific notation: 0.00000631

2) Simplify. Write the answer using positive exponents only. (5 pts)

3) Simplify. Write the answer using positive exponents only. (5 pts)

4) Simplify. Write the answer using positive exponents only. (5 pts)

5) Perform the indicated operations and simplify: (5 pts)

6) Perform the indicated operations and simplify: (5pts)

7) Perform the indicated operations and simplify: (5 pts)

8) Factor completely. Show work following the method discussed in Sections 6.1 and 6.3 of our text, and show the check by re-multiplication of the factors. If the polynomial is not factorable, write \"prime.\" (5 pts)

9) Solve the equation by the method of factoring. Use the factoring technique discussed in Section 6.4 of our text, and solve following the methods discussed in Section 6.7. (5 pts)

10) Solve the equation by the method of factoring. Use the factoring technique discussed in Section 6.4 of our text, and solve following the methods discussed in Section 6.7. (5 pts)

BONUS::::::

Perform the indicated operations and simplify. Show work to support your answer. (5 pts)

Solution

1 a) 360,559,112 = 3.60559112 x 10⁸

   b) 0.00000631 = 6.31x 10^-6

  c) 2.06 x 10⁶ = 2060000

d) 8.004 x 10^-7 = 0.0000008004

e) 2^-3 - 5⁰ + 8^-1 = 1/2³ -1 + 1/8 = 1/8 - 1 + 1/8 = 2/8 - 1 = 1/4 - 1 = -3/4 = - 0.75

2. ( 2x³ y^-2 z)( 5x⁴ y² z⁷) = 2*5 (x³⁺⁴ y^-2+2 z¹⁺⁷) = 10x⁷z⁸ ( as  y^-2+2 = y⁰ = 1; p^a * p^b = p^a+b)

3. (2x⁵ y^-3)⁴ = 2⁴x^5*4 y^-3*4 = 16x²⁰ y^-12 = 16x²⁰/y¹²

4. ( 2a^-1/3b^-3)^-2 = (2b³/ 3a²)^-2 =( 2^-2 b^-6/ 3^-2 a^-4) = ( 3² a⁴/ 2² b⁶) = 9a⁴/ 4b⁶)

5. (3x²y -4x) + (5x²y -8) - (4 -11x) = 3x²y + 5x²y -4x+ 11x - 8 - 4 = 8x²y +7x -12

6. (6x -4y²)(6x + 4y²) = (6x)² -(4y²)² = 36x² - 16y⁴ [ as (a - b)(a + b) = a² - b²; here a = 6x and b = 4y²)

7. (3y -2)( 4y² +3y -2) = (3y -2)(4y²) + (3y -2)² = 12y³ -8y² + ( 9y² - 2*3y*2 + 4) = 12y³ - 8y² + 9y² -12y + 4 = 12y³ + y² -12y + 4 [ as (a -b)² = a² - 2ab + b²; here a = 3y and b = 2)

8. 3n² -27n + 24 = 3(n² - 9n + 8) = 3 ( n² - 8n - n + 8) = 3 [ n(n -8) - 1(n -8)] = 3(n - 8)(n -1).

Recheck: 3(n - 8)(n -1) = 3 [ n(n -1) -8(n -1)] = 3[ n² - n - 8n + 8] = 3( n² -9n + 8) = 3n² -27n + 24

9. 2x² +9x -5 = 0 or, 2x² + 10x - x - 5 = 0 or, 2x (x +5) -1(x + 5) = 0 or, (x + 5) (2x -1) = 0 . Therefore, either x + 5 =0 so that x = - 5 or, 2x - 1 = 0 so that x = 1/2. Thus, either x = -5 or x = 1/2.

10. 30x² = 3x + 9 or, 30x² - 3x -9 = 0 or, 10x² -x - 3 = 0 or, 20x² - 2x - 6 = 0 or, 20x² + 10x - 12x - 6 = 0 or,

10x( 2x + 1) - 6( 2x + 1) = 0 or, ( 2x + 1) ( 10x -6) = 0. Therefore, either 2x + 1 = 0 so that x = - 1/2 or, 10x - 6 = 0 so that x = 6/10 = 3/5.Thus, eithe r x = - 1/2 or x = 3/5.

Bonus:

(x -y)² - ( x + y) (x -y) = x² -2xy + y² - (x² - y²) = x² - x² -2xy + y² + y² = 2y² - 2xy = 2y( y -x)