Question

Please help! i was never taught this and my teacher is no help.

Answer 1

Step-by-step explanation:

To factor a GCF, you just see the greatest common factor all the variables have in the equation.

1. $24x^4y-9x^3y^3-12x^3y^2$ <- here, for example, you can see that all the numbers in front of the variables can be divided by 3, so that is your first GCF.

* you can only take out what you have, not what you don't have, btw.

You can also see (by the powers) that you can take out x^3 because all the x's have at least 3 x's multiplied with each other.

And, you can take out only one y since there is at least one y in every set of variables.

Once you take out all of these GCF's, you divide each variable by them. This is because when you take them out, you're still going to be multiplying the whole set of variables by the GCF's, so they should always equal their original form.

I hope this step by step explanation for #1 is enough for all of the problems, if you need further help please feel free to comment! :)

Answer:

1. $3x^3 y (8 x - 3y^2 -4y )$

2. $2y ( 12x^2 - 9xy - 1 )$

3. $6y^2 ( 4x^3 - 3xy + 2y )$

4. $3(8x^3 - 3x^2y^2 -4y)$

5. $4xy ( 6x^2y + 4x + 3y^3)$

6. $6x(4x^2y - 3x + 2y^2)$

7. $2xy^2 (12x + 9y^2 -y )$

8. $4x^2y (6x + 4y + 3 )$