7x^3 - x + 1 = x^3 + 3x^2 + x?

Question

How can i factor this? show work and explain please.

Answer 1

7x^3 - x + 1 = x^3 + 3x^2 + x

7x^3 - x^3 - 3x^2 - x - x + 1 = 0

6x^3 - 3x^2 - 2x + 1 = 0

(6x^3 - 3x^2) - (2x - 1) = 0

3x^2(2x - 1) - 1(2x - 1) = 0

(2x - 1)(3x^2 - 1) = 0

2x - 1 = 0

2x = 1

x = 1/2 (0.5)

3x^2 - 1 = 0

3x^2 = 1

x^2 = 1/3

x = ±1/(√3)

∴ x = 1/2 (0.5) , ±1/(√3)

Answer 2

7x^3 - x + 1 = x^3 + 3x^2 + x (subtract x^3, 3x^2, and x from both sides)

6x^3 - 3x^2 - 2x + 1 = 0 (group)

(6x^3 - 3x^2) - (2x - 1) = 0 (factor out 3x^2 from first group)

3x^2(2x - 1) - 1(2x - 1) = 0 (place in factor form)

(3x^2 - 1)(2x - 1) = 0 <===ANSWER

How to factor by grouping: http://www.math.unc.edu/Faculty/mccombs/...