Algebra - factoring. Please, help me!

Hi, please explain how you do it step by step. Thank you so much.
y^3 + y^2 - 10y - 6 = 0.

y^3 + y^2 - 10y - 6 = 0.

Use the rational root theorem to discover a factor...try (x - 3)

then use synthetic division to get the quadratic factor...

3]..1.....1.....- 10.....- 6
_______3___12____6
.....1.....4.......2.......0

(x - 3)(x^2 + 4x + 2) = 0

You can find the roots from the quadratic factor, right ? I hope so...Go for it.

use vanishing method.. Look if u put y=3,then the eqn is being satisfied.So (y-3) is a function f that eqn.. So, y^2(y-3)+4y(y-3)+2(y-3)=0or,(y-3)(y^2+4y… the rest..

it can b done by remainder theorem


f(3)=0
so y-3 is a factr

Now divide f(y) by y-3

3 | 1 1 -10 -6
3 12 6
......................................…
1 4 2 0

Quotient=y^2 +4y+2

f(y)=(y-3)(y^2 +4y+2)

(y-3)(y^2+4y+2)=0

y=3

a=1 b=4 c=2

-4+/- sq rt 4^2-4(1)(2)/2
-4+/- sq rt 16-8/2
-4+/- sq rt 8/2
-4+/- 2 sq rt 2/2
-2+/- sq rt 2

y=3 y=-2+ sq rt 2 y=-2- sq rt 2