Question 997279
{{{p(x) = 25x^5 -95x^4 + 139x^3 -97x^2 + 32x - 4 }}}...to factor it, first write {{{-95x^4}}} as {{{-20x^4-75x^4}}}, {{{139x^3}}} as {{{4x^3+ 60x^3+75x^3}}}, {{{-97x^2}}} as {{{-60x^2-25x^2}}}, and {{{32x}}} as {{{12x+20x}}}, then group

{{{p(x) = 25x^5 -20x^4 + 4x^3 -75x^4+ 60x^3-12x^2+75x^3-60x^2+12x-25x^2+20x-4}}}

{{{p(x) = (25x^5 -20x^4 + 4x^3) -(75x^4 -60x^3+12x^2)+(75x^3-60x^2+12x)-(25x^2-20x+4)}}}

{{{p(x) =x^3 (25x^2 -20x + 4) -3x^2(25x^2 -20x+4)+3x(25x^3-620x+4)-(25x^2-20x+4)}}}

{{{p(x) =(x^3-3x^2+3x-1) (25x^2-20x+4)}}}

{{{p(x) =(x-1)^3 (5x-2)^2}}}


so, zeros are:

if {{{0=(x-1)^3 }}}=>{{{x=1}}}-the multiplicity of this real zero is {{{3}}}

if {{{0=(5x-2)^2}}}=>{{{5x-2=0}}}=>{{{x=2/5}}}-the multiplicity of this real zero is {{{2}}}

{{{ graph( 600, 600, -4, 4, -5, 5, (x-1)^3 (5x-2)^2) }}}