Grouping/special factoring/synthetic dividing

Question

Y^3 - 27

use synthetic dividing and the remainder theorem

-2/3 if f(x) = -6x^3 + 8x^2 - x - 6

thank you

Answer 1

By using synth/div l got:

(2/3)⌋-6x^3+8x^2-x-6

(2/3)⌋-6+8-1 -6

__-4+8/3+10/9____

-6+4+5/3-44/9 so:-6x^3+4x^2+1.66x-4.88/.66

1) bring down the -6

2) multiply it by the divisor

3) subtract it from the 8.

4) repeat

5) put in the multiples.

Answer 2

y³ - 3³ = (y - 3)(y² + 3y + 9) By the cube factoring formula

-2/3 | -6 8 -1 -6

4 -8 6

-6 12 -9 0