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

Expert Answers
violy eNotes educator| Certified Educator

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).

oldnick | Student

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.