factor -8x^3 - 2x^2 - 12x - 3 by grouping. what is the resulting expression? (2x^2 - 3)(4x + 1) (-2x^2…

factor -8x^3 - 2x^2 - 12x - 3 by grouping. what is the resulting expression? (2x^2 - 3)(4x + 1) (-2x^2 - 3)(-4x + 1) (2x^2 - 3)(-4x + 1) (-2x^2 - 3)(4x + 1)

factor -8x^3 - 2x^2 - 12x - 3 by grouping. what is the resulting expression? (2x^2 - 3)(4x + 1) (-2x^2 - 3)(-4x + 1) (2x^2 - 3)(-4x + 1) (-2x^2 - 3)(4x + 1)

Answer

Answer:

D. ((-2x^{2}-3)(4x + 1))

Explanation:

Step1: Agrupar términos

(-8x^{3}-2x^{2}-12x - 3=(-8x^{3}-2x^{2})+(-12x - 3))

Step2: Factor común en cada grupo

Factorizando (-8x^{3}-2x^{2}) obtenemos (-2x^{2}(4x + 1)), y factorizando (-12x - 3) obtenemos (-3(4x + 1)). Entonces la expresión es (-2x^{2}(4x + 1)-3(4x + 1)).

Step3: Factor común general

Tomando ((4x + 1)) como factor común, tenemos ((4x + 1)(-2x^{2}-3)=(-2x^{2}-3)(4x + 1)).