Question 1170466

Give the factored form of the polynomial equations.

1.

{{{x^3-2x^2-5x+6=0}}}
{{{x^3+x^2-3x^2-2x-3x+6=0}}}
{{{(x^3-3x^2)+(x^2-3x)-2(x-3)=0}}}
{{{(x - 3) (x^2+x -  2) = 0}}}
{{{(x - 3) (x^2+2x-x -  2) = 0}}}
{{{(x - 3) ((x^2+2x)-(x + 2)) = 0}}}
{{{(x - 3) (x(x+2)-(x + 2)) = 0}}}
{{{(x - 3) (x - 1) (x + 2) = 0}}}



2.


{{{x^3-x^2-10x-8=0}}}
{{{x^3-4x^2+3x^2-12x+2x-8=0}}}
{{{(x^3-4x^2)+(3x^2-12x)+(2x-8)=0}}}
{{{x^2(x-4)+3x(x-4)+2(x-4)=0}}}
{{{(x - 4) (x^2 + 3x + 2) = 0}}}
{{{(x - 4) (x^2 + 2x +x+ 2) = 0}}}
{{{(x - 4) (x + 1) (x + 2) = 0}}}


give the factored for of

1.

{{{2x^4+5x^3-5x-2=0}}}, given that one root is {{{1}}}, so factor out {{{x-1}}}
{{{2x^4-2x^3+ 7x^3- 7x^2+ 7 x^2 - 7 x + 2x   - 2=0}}}
{{{(2x^4-2x^3)+ (7x^3- 7x^2)+ (7 x^2 - 7 x) + (2x   - 2)=0}}}
{{{2x^3(x-1)+ 7x^2(x- 1)+ 7 x(x - 1) + 2(x   - 1)=0}}}
{{{(x - 1) (2x^3 + 7x^2 + 7 x + 2) = 0}}}
{{{(x - 1) (2x^3 +2 x^2+ x^2+ 2 x+4x^2+4x  + 2 + x+2) = 0}}}
{{{(x - 1) ((2x^3 +2 x^2)+ (x^2+ x )+(4x^2+4x ) + (2x+2)) = 0}}}
{{{(x - 1) (2 x^2(x +1)+ x(x+ 1 )+4x(x+1 ) +2 (x+1)) = 0}}}
{{{(x - 1) (x + 1)  (2 x^2 + x+4x+2) = 0}}}
{{{(x - 1) (x + 1)  ((2 x^2 +4x)+ (x+2)) = 0}}}
{{{(x - 1) (x + 1)  (2x(x +2)+ (x+2)) = 0}}}
{{{(x - 1) (x + 1) (x + 2) (2 x + 1) = 0}}}