Remove the greatest common factor. A) 3a^2+3a B)21ab-14ab^2

Expert Answers
violy eNotes educator| Certified Educator

For letter a, since 3 is in both of the terms, 3 will be included in the gcf. 

Fo the literal factors, we choose the one with the least amount of exponent. 

We compare the exponent of a^2 and a. 

1 < 2. Hence, a will be included in our gcf. Multiplying 3 and a:  3 * a = 3a. So, our gcf = 3a. 

We can set it up like this: 

3a^2 + 3a = 3a(__ + ___)

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

3a^2/3a = a

For the second blank, divide the second term by the gcf. 

3a/3a = 1 

Hence, answer for part A is: 3a(a + 1).

For part b, think of a number which both 14 and 21 is divisible with. 

We can prime factorize both of them first. 

14 = 7 * 2  and 21 = 7 * 3 

Hence, gcf = 7.

For the literal factors we choose the one with the least amount of exponent. 

So, for the literal factors gcf = ab. 

We then, factor out 7ab. 

21ab - 14ab^2 = 7ab(___ + ____)

For the first blank: 21ab/7ab = 3

For the second blank: -14ab^2 = 7ab = -2b.

So, final answer for part B is 7ab(3 - 2b).

oldnick | Student

`3a^2+3a=3a(a+1)`   (1)


 `21ab-14ab^2=7ab(3-2b)`  (2)

the greater commmon divisor  beteween  (1) and (2) is a, so that:

`3(a+1)`      (1)

`7b(3-2b)`  (2)