Question

Hi, using factoring by grouping, solve
6x^3-6x^2-x+1

Answer 1

okay let us observe what is similar here:
6x^3-6x^2-x+1, i can factor out 6x^2 from the first two terms:
6x^2(x-1) - x+1

Answer 2

check that 1 is a solution to
\[6x^3-6x^2-x+1=0\] and then divide by
\[(x-1)\] to get
\[(x-1)(6x^2-1)\]

Answer 3

6x^2(x-1) - x+1 i can factor out the - sign from the next two terms:
6x^2(x-1) - (x-1), now I can factor out the whole x-1
(x-1) (6x^2-1)

Answer 4

so zeros are
\[1,-\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}\]

Answer 5

x-1=0
6x^2-1=0
x=1
6x^2=1, x^2 = 1/6 => x1,2 = +or- sqrt(6)/6 and both me and satellite are right!