Question

Factor the GCF: 9a4b3 + 24a3b2 − 15a2b

A) 3a2b(3a2b2 + 8ab − 5)

B) 3a2b3(3a2 + 8ab − 5)

C) 3a2b(3a2b + 8ab − 5b)

D) 3ab(3a3b2 + 8ab − 5a)

Answer 1

9a^4b^3 + 24a^3b^2 - 15a^2b

3a^2b(3a^2b^2 + 8ab - 5) <==

Answer 2

The correct option is A.

Explanation:

The given expression is,

`9a^4b^3+24a^3b^2-15a^2b`

The greatest common factors of two numbers is the greatest number that divides both numbers completely.

We can write each term as,

`9a^4b^3=3* 3* a* a* a* a* b* b* b`

`24a^3b^2=2* 2* 2* 3* a* a* a* b* b`

`15a^2b=3* 5* a* a* b`

We can say that the factors 3, a, a and b are common in all the terms, therefore the greatest common factor is 3a²b.

Take 3a²b as GCF,

`9a^4b^3+24a^3b^2-15a^2b=3a^2b(3a^2b^2+8ab-5)`

Therefore the correct option is A.