If the polynomial 6x6 - 4x5 + 9x - 6 is to be factored by grouping, which step should be taken?

I think you're trying to say 6x^6-4x^5+9x-6. ^ Is a symbol that means the number after it is an exponent.

First step, find the gcf (greatest common factor) between the first two parts. The gcf of 6x^6-4x^5 is 2x^5.

Now take it out. You get

2x^5 (3x-2)

If you expand that equation, you will get 6x^6-4x^5 which is why you know it's correct.

Now do the same for the second half.

The gcf for the second two parts is 3.

3 (3x-2)

Notice anything? Yep, in both of them, after you take out the gcf, you get (3x-2)

Now, you combine them into one equation

2x^5 (3x-2) + 3 (3x-2)

Then you do this

(2x^5+3) (3x-2)

That's your factored form.