Question 1170975

1.

{{{(2x^2-5x-3)^2(9x^2-24x+16)^3(2x^2+13x+21)=0}}}

first factor {{{(2x^2-5x-3)^2}}}

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

now factor {{{(9x^2-24x+16)^3}}}
{{{(9x^2-24x+16)^3=(3x)^2-24x+4^2)^3 =((3 x - 4)^2)^3=(3 x - 4)^6}}}

and factor {{{(2x^2+13x+21)=2x^2+7x+6x+21=(2x^2+6x)+(7x+21)= 2x(x+3)+7(x+3)=(x + 3) (2 x + 7)}}}

combine all together

{{{(2x + 1)^2*(x - 3)^2*(3 x - 4)^6*(x + 3) (2 x + 7)=0}}}


2.

{{{(x^2+4x)^2(3x^2-17x-6)^2(4x^2+9x-9)^3=0}}}

factor{{{(x^2+4x)^2=(x(x+4))^2=x^2(x+4)^2}}}

factor {{{(3x^2-17x-6)^2= (3x^2-18x+x-6)^2 =((3x^2-18x)+(x-6))^2=(3x(x-6)+(x-6))^2 =(3 x + 1)^2 (x - 6)^2}}}

factor {{{(4x^2+9x-9)^3=(4x^2+12x-3x-9)^3=((4x^2+12x)-(3x+9))^3= (4x(x+3)-3(x+3))^3=((4x-3)(x+3))^3 = (4x - 3)^3 (x + 3)^3}}}

all together:

{{{x^2(x+4)^2*(3 x + 1)^2 (x - 6)^2*(4x - 3)^3 (x + 3)^3=0}}}