Question 1180384


{{{P(x) = x^4 + 2x^3 - 2x^2 - 3x +2}}}


{{{x^4 + 2x^3 - 2x^2 - 3x +2=0}}}...factor

{{{x^4 -x^3+3x^3- 3x^2+x^2-x- 2x+2=0}}}

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

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

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

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

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

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

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

solutions:

{{{(x - 1)  = 0}}}=>{{{x=1}}}

{{{(x + 2)= 0}}}=>{{{x=-2}}}

{{{ (x^2 + x - 1) = 0}}}...use quadratic formula

{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}

{{{x=(-1+-sqrt(1^2-4*1*(-1)))/(2*1)}}}

{{{x=(-1+-sqrt(1+4))/2}}}

{{{x=(-1+-sqrt(5))/2}}}

solutions:

{{{x=-1/2+sqrt(5)/2}}}

{{{x=-1/2-sqrt(5)/2}}}