1 - y^(3)=
1^(3) - (3) =
This factors to
(1 - y)(1^(2) + y + y^(2))
More simply written as
( 1 - y)(1 + y + y^(2))
A completely factored form is one which is composed of product of factors and can't be factorized further. Let us consider two examples: x2 - 4x + 4 is not a factored form because it can be factored as (x - 2)(x - 2). (x +1)(x2 - 4x + 4) is also not a factored form because x2 - 4x + 4 can be factored further as (x - 2)(x - 2). So, the completely factored form is (x + 1)(x - 2)(x - 2).
2x(1-5)
It is (x-1)(x-1) when factored
2(a+b) is 2a plus 2b in factored form.
3(x - 1)( x + 8)
-2
27-y3 factored completely = 24
5
A completely factored form is one which is composed of product of factors and can't be factorized further. Let us consider two examples: x2 - 4x + 4 is not a factored form because it can be factored as (x - 2)(x - 2). (x +1)(x2 - 4x + 4) is also not a factored form because x2 - 4x + 4 can be factored further as (x - 2)(x - 2). So, the completely factored form is (x + 1)(x - 2)(x - 2).
6x2+5x+1 = (3x+1)(2x+1) when factored
(1-y)(1+y)
It is: (3x+1)(x-1)
That can't be factored. In general, a binomial (i.e., a polynomial with two parts) can only be factored if both parts have a common factor, or if you can express it as the sum or difference of squares, cubes, etc.
3a2b(2b2-1)
2x(1-5)
You can't know if a general polynomial is in factored form.
Let's say y1, y2, and y3 are zeros. Set up an expression like this (x-y1)(x-y2)(x-y3) [This is factored form] and then multiply carefully. That works with any number of roots. If 0 is a root, add an x by itself to the beginning of the factored form expression. Also, imaginary roots come in twos. Therefore, if given i as a root, you need (x-i)(x+i). If you have something in x + yi form for a root, you'll need the complex conjugate. That would make (x-(a+bi))(x-(a-bi))