Question 1170428

A.Give the factored form of the polynomial equations

{{{x^3+2x^2-23x-60=0}}}

 {{{x^3 + 7x^2+ 12x-5x^2-35x-60 = 0}}}

{{{( x^3-5x^2) + (7x^2-35x)+ (12x-60) = 0}}}

{{{x^2( x-5) + 7x(x-5)+ 12(x-5) = 0}}}

{{{ (x - 5) (x^2 + 7x+ 12) = 0}}}

{{{(x - 5) (x^2 + 4x +3x+ 12) = 0}}}

{{{(x - 5) ((x^2 + 4x) +(3x+ 12)) = 0}}}

{{{(x - 5) (x(x + 4) +3(x+ 4)) = 0}}}

{{{(x - 5) (x + 3) (x + 4) = 0}}}



B. {{{x^5-5x^4-3x^3+15x^2-4x+20=0}}}, given that one root is {{{2}}}; since given root, first group to factor out {{{x-2}}}


{{{x^5-5x^4-3x^3+15x^2-4x+20=0}}}

{{{x^5-3x^4  -9x^3  - 3x^2-10x  - 2x^4+6x^3+18x^2+6x +20  =0}}}

{{{(x^5 - 2x^4)  -(3x^4  -6x^3)-(9x^3 -18x^2) - (3x^2-6x) -(10x-20)      =0}}}

{{{x^4(x - 2)  -3x^3(x  -2)-9x^2(x -2) -3x (x-2) -10(x-2)      =0}}}

{{{(x - 2) (x^4 - 3x^3 - 9x^2 - 3x - 10) = 0}}}

{{{(x - 2) (x^4 +2x^3- 5x^3+x^2 - 10x^2+2x - 5x - 10) = 0}}}

{{{(x - 2) ((x^4 - 5x^3)+(2x^3 - 10x^2)+(x^2 - 5x)+(2x - 10)) = 0}}}

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

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

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

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

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