Factor the GCF

Question

Factor the GCF: 9a²b³ + 24a³b² - 15a²b 

 

(This question is on my homework guide and I do not know how to solve it. Can someone please show me the steps of solving it so I can know how to next time?) :-) 

Answer 1

9a²b³+24a³b²-15a²b

first find the GCF of 9, 24, and 15

9=3x3

24=2x2x2x3

15=3x5

what is common to all three factorizations ? 3 is common

find the GCF of a², a³, and a²

a²=axa

a³=axaxa

a²=axa

what is common to all three factorizations ? axa or a²

(I could have said to pick the highest power of "a" common to all three)

find the GCF of b³, b², and b

b³=bxbxb

b²=bxb

b=b

what is common to all three factorizations? b

(I could have said to pick the highest power of "b" common to all three)

now multiply the three answers together

3a²b

now divide this into each of the terms, or in other words, what do you multiply this 3a²b to get each of the three terms ?

3a²b(3b²+8ab-5)