(08.01, 8.02 MC) An expression is shown below:
4x3 - 20x2 +36x - 180
Part A: Rewrite the expression so that the GCF is factored completely. (4 points)
Part B: Rewrite the expression completely factored. Show the steps of your work. (6
points)
(10 points)

Step-by-step explanation:

A) We observe that each coefficient is divisible by 4. The GCF of the terms is 4.

  4x^3 - 20x^2 +36x - 180 = 4(x^3 -5x^2 +9x -45)

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B) We further observe that the coefficients of each pair are in the ratio 1:-5, so we can factor pairwise:

  = 4(x^2(x -5) +9(x -5)) = 4(x^2 +9)(x -5) . . . . factored completely in reals

The quadratic factor x^2+9 can be factored further if complex numbers are used:

  = 4(x -3i)(x +3i)(x -5) . . . . factored completely in complex numbers

Comment on the quadratic factor

The term x^2 +9 can be considered to be the difference of squares:

  x^2 +9 = x^2 -(-9)

  = x^2 -(3i)^2

  = (x -3i)(x +3i)

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068

600,000,000,000, or 6e14

step-by-step explanation: