factor help?

Question

factor the greatest common factor

10x^3(2x-3y)-15x^2(2x-3y)

factor by grouping...?

5xy^2+5y^2+3ax+3a

3x^3+2x^2-27X-18

Factor trinomial

y^2-y-6

Answer 1

The above are all either wrong or do not show proper work...

To start with the last query:
y^2 - y - 6=0
(y-3)(y+2)=0
There is no real simple way to explain this except by simply saying F.O.I.L., which you surely are familiar with.

Now to factor by grouping:
5xy^2 + 5y^2 + 3ax + 3a = 0 Next, group those with similar numbers/variables
(5xy^2 + 5y^2) + (3ax + 3a) = 0 Next, factor out similar terms
5y^2(x + 1) + 3a(x+1) = 0 Next, use combination to simplify to two parenthetical terms
(5y^2 + 3a)(x+1) = 0 And that is your solution.

The other one to be factored by grouping: follow the same path as above. you need to get two terms in parentheses to be the same.
3x^3 + 2x^2 - 27x - 18 = 0
(3x^3 - 27x) + (2x^2 - 18) = 0
3x(x^2 - 9) + 2(x^2 - 9) = 0
(3x + 2)(x^2 - 9) = 0
(3x + 2)[(x+3)(x-3)] = 0

And now to factor the greatest common factor:
(10x^3 - 15x^2)(2x - 3y) = 0
5x^2(2x - 3)(2x - 3y) = 0

I hope this helps, and wish you all the best.

Answer 2

factor the greatest common factor

10x^3(2x-3y)-15x^2(2x-3y)
GCF = 5x^2(2x-3y)
To factor, divide by GCF - leaving you
2x +3

factor by grouping...?

5xy^2+5y^2+3ax+3a
5y^2(x+1) + 3a(x+1)
Factor Out (x+1_
5y^2 + 3a

Factor trinomial
y^2-y-6
(y + 2)(y - 3)

Answer 3

GCF is (2x-3y)*5x^2 =>5x^2(2x-3y)(2x-3)
5y^2(x+1)+3a(x+1)=5y^2(x+1)
3x(x^2-9)+2(x^2-9)=3x^2(x+3)(x-3)
(y-3)(y+2)

Answer 4

1) 5x^2(2x-3y)(2x-3) (the 5x^2(2x-3y) is the GCF)

2) (5y^2+3)(x+1)

3) (y-3)(y+2)