Question

Factor out the GCF from the polynomial..... 14y^7+12y^2 . The correct answer to this is 2y^2(7y^5+6) . Can someone explain the process to do this, please? thanks...

Answer 1

first find the GCF of 14 and 12
this is the highest number which will divide exactly into 12 and 14
you can do this by factoring each number: (prime factors}
12 = 2*2*3
14 = 2*7

check for matching numbers:- there is one matching number 2

2 is the required GCF

are you OK with this explanation?

Answer 2

where do the other numbers come into play?

Answer 3

now deal with the 2 terms n 'y':

y^7 = y*y*y*y*y*y*y
y^2 = y*y

y^2 is the GCF

Answer 4

you don't need to worry about the other numbers when finding the GCF - only the ones that match

Answer 5

to complete the factoring process you divide the GCF ( 2y^2) into the 2 terms of the original expression

14y^7 / 2y^2 = 7y^5
+ 12y^2 / 2y^2 = + 6

to give

2y^2(7y^5 + 6)

Answer 6

ok?

r u familiar with division of terms containg powers

eg y^3 / y^2 ?

you subtract the powers so

y^3 / y^2 = y^(3 - 2) = y^1 = y

Answer 7

stilll kinda confused..where does the 6 come from

Answer 8

12 / 2 = 6
y^2 / y^2 = 1

Answer 9

or you can treat it this way ( this is sometimes called 'cancelling'):