You can put this solution on YOUR website! 1)
(x^3-6x^2+11x-6)/(x-1) Long division or synthetic division.
=x^2-5x+6
=(x-3)(x-2)
.
2)
x^2+6x+9=0
(x+3)^2=0
x=-3
.
3)
2x^2+5x-12=0
2*-12=-24... 8 and -3 are factors of -24 that when added equal 5.
2x^2+8x-3x-12=0
2x(x+4)-3(x+4)=0
(2x-3)(x+4)=0
2x=3
x=3/2
x=-4
.
4)
3x^3=12x
3x^3-12x=0
3x(x^2-4)=0
3x(x+2)(x-2)=0
x=0, x=-2, x=2
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5)
(2x-1)(3x+5)=5
6x^2+7x-5=5
6x^2+7x-10=0
6*-10=-60... 12 and -5 are factors of -60 whose sum is 7.
6x^2+12x-5x-10=0
6x(x+2)-5(x+2)=0
(6x-5)(x+2)=0
6x=5
x=5/6
x=-2
.
Ed
