how can i?

Question

how can i factore this:

8x^3+12xy+6x+1

and

8x^3+1

Answer 1

no idea......

Answer 2

For the second one, you can treat it like long division. It looks like
2x+1 is a factor.

Set up a long division problem
8x^3 +1 div by 2x+1 is 4x^2 = 1- 4x^2 (that's the diff of two squares)

So,

(2x+1)(1+2x)(1-2x) = (1-2x)(1+2x)^2
(something's not right, this would give an negative coeff of 8x^3)

You should check it.

Note that you can do long division with polynomials just like numbers.

Answer 3

8x^3 + 12xy + 6x + 1 =
8x^3 + 6x(2y + 1) + 1
. . . . 4x^2 - 2x + 1
2x + 1)8x^3. . . . . . . . + 1
. . . . 8x^3 + 4x^2
. . . . . . . . .- 4x^2
. . . . . . . . .- 4x^2 - 2x
. . . . . . . . . . . . . . 2x + 1
. . . . . . . . . . . . . . 2x + 1

(2x + 1)(4x^2 - 2x + 1) + 6x(2y + 1)

4x^2 - 2x + 1 =
4x^2 - 2x + 1/4 + 1 - 1/4 =
(2x - 1/4)^2 + 3/4 =
(2x - 1/4 + (1/2)√3)(2x - 1/4 - (1/2)√3)

8x^3 + 12xy + 6x + 1 =
(2x + 1)(2x - 1/4 + (1/2)√3)(2x - 1/4 - (1/2)√3) + 6x(2y + 1)

8x^3 + 1 =
(2x + 1)(2x - 1/4 + (1/2)√3)(2x - 1/4 - (1/2)√3)

Answer 4

8x³-1 = 2³x³ - 1³ = (2x - 1)(4x²+2x+1)
(i will get back to you on the other one in a sec)

Answer 5

8x^3+1
8x^3 = -1
x^3 = -1/3
x = cube root of -1/3 = -0.69