Answer:
Lucas groups the polynomial (12x^3 + 8x) + (–6x^2 – 4) to factor → 2 (2 x - 1) (3 x^2 + 2)
Step-by-step explanation:
Factor the following:
12 x^3 - 6 x^2 + 8 x - 4
Hint: | Factor out the greatest common divisor of the coefficients of 12 x^3 - 6 x^2 + 8 x - 4.
Factor 2 out of 12 x^3 - 6 x^2 + 8 x - 4:
2 (6 x^3 - 3 x^2 + 4 x - 2)
Hint: | Factor pairs of terms in 6 x^3 - 3 x^2 + 4 x - 2 by grouping.
Factor terms by grouping. 6 x^3 - 3 x^2 + 4 x - 2 = (6 x^3 - 3 x^2) + (4 x - 2) = 3 x^2 (2 x - 1) + 2 (2 x - 1):
2 3 x^2 (2 x - 1) + 2 (2 x - 1)
Hint: | Factor common terms from 3 x^2 (2 x - 1) + 2 (2 x - 1).
Factor 2 x - 1 from 3 x^2 (2 x - 1) + 2 (2 x - 1):
Answer: 2 (2 x - 1) (3 x^2 + 2)
