Question 400214
{{{20x^6-7x^5-6x^4-500x^4+175x^3+150X^2=x^4(20x^2-7x-6)-25x^2(20x^2-7x-6)=(20x^2-7x-6)*(x^4-25x^2)=x^2(20x^2-7x-6)*(x^2-25)}}}
for the factor {{{20x^2-7x-6=20(x-x1)(x-x2)}}}
{{{20x^2-7x-6=0}}}
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{x = (-(-7)+- sqrt( (-7)^2-4*20*(-6) ))/(2*20) }}} 
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{{{x1 = (7+ 23)/40 }}}______ {{{x2= (7- 23)/40 }}} 
{{{x1 = 3/4 }}}______ {{{x2= - 2/5 }}} 
{{{20x^2-7x-6=20(x-3/4)(x+2/5)=4*(x-3/4)*5*(x+2/5)=(4x-3)(5x+2)}}}
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for the factor {{{(x^2-25)}}}
formula {{{a^2-b^2=(a-b)*(a+b)}}}
 {{{(x^2-25)=(x)^2-(5)^2=(x-5)(x+5)}}}
So
{{{x^2(20x^2-7x-6)*(x^2-25)=x^2(4x-5)(5x+2)(x-5)(x+5)}}}