# Remove the greatest common factor. A)6b(2a-3c)-5d(2a-3c) B)4a^3(a-3b)+(a-3b)

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For part a, the terms are 6b(2a - 3c) and -5d(2a - 3c).

Therefore, gcf is (2a - 3c).

We can set it up like this:

6b(2a - 3c) - 5d(2a - 3c) = (2a - 3c)(____ + _____).

For the first blank, we divide the first term by the gcf.

6b(2a - 3c)/(2a - 3c) = 6b

We do the same principle for the second blank.

- 5d(2a - 3c)/(2a - 3c) = -5d.

So, our **final answer for part a will be (2a - 3c)(6b - 5d)**.

For part b, we gcf is (a - 3b).

We can set it up like this:

4a^3(a-3b)+(a-3b) = (a - 3b)(___ + ____)

We do the same process as what we did on part a.

So, for the first blank: 4a^3(a-3b)/(a-3b) = 4a^3

For the second blank, (a-3b)/(a-3b) = 1.

Hence, **the final answer for part b is (a - 3b)(4a^3 + 1)**.

re-write two polymoms.

`(6b-5d)(2a-3c)` `(a-3b)(4a^3+1)`

Now if was an common divisor `d(x)!=1` , since is clear the components of both polynoms haven't common factors , then `d(x)` divides one only out of them.

Suppose `d(x)| (2a-3c)` i.e, so is to be of first degree polyonom that contents variable `c` , but isn't possible for the polynom:`(a-3b)(4a^3+1)` hasn't this term.

At the same if `d(x)|(6b-5d)` ,for neither `d ` appears in the second polynom , so GCD is to be 1.