(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)

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)  

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step-by-step explanation: