Answer:
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
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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)
