Question

6. Factor the following polynomial:
12y^5-8y^3+24y^2
A. 8y(2y^4-y^2+3y)
B. 4y^2(3y^3-2y+6)
C. 4y(3y^5-2y^3+6y^2)
D. 4y(3y^4-2y^2_6y)

@welshfella

Answer 1

ummmmm.

Answer 2

Hahahaha

Answer 3

are you familiar with prime factors?

what prime factors do each of the terms share?

Answer 4

Are you talking about like terms?

Answer 5

no i mean ify ou have the term
12xy^2

the prime factors of this would be 2,2,3,x,y,y

Answer 6

breaking it up into its smallest components, which in terms of numbers, would be prime numbers

Answer 7

I dont know that

Answer 8

ok, then use division rules

any even number can be divided by 2 right?

Answer 9

Its 1 answer down from A. :)

Answer 10

Yes

Answer 11

so if you look at all your terms, 12y^5, -8y^3, and 24y^2

are all these terms even?

Answer 12

Uh no

Answer 13

you need to find the GCF of the 3 terms
do you know what the GCF is?

Answer 14

No

Answer 15

the greatest common factor
First consider the numbers
GCF of 12,8 and 24 is 4 because its the largest number which divides into all 3 numbers

Answer 16

Next you nee to find the GCF of y^5 , y^3 and y^2

Answer 17

one of those will divide exactly into all 3 Which one?

Answer 18

D: I dont know

Answer 19

do you think it might be y^2?

y^2 /y^2 = 1
will y^2 divide into y^3 and y^5?

Answer 20

recall when you divide exponential terms you subtract the exponents

Answer 21

I would think its y^5

Answer 22

No the GCF is not y^5 because it is not a factor of y^2 or y^3
- but y^2 is a factor of both

y^5 /y^2 = y^3
y^3 / y^2 = y


so y^2 is the GCF

Answer 23

Oh I see

Answer 24

combining this with the 4 we have
4y^2 which is the GCF of the 3 terms in the original question

Answer 25

we can also see that y^2 is the GCF if we expand the terms

y^5 = y * y* y * y * y

y^3 = y * y * y

y^2 = y * y

We see that y^2 will divide into all 3.

Answer 26

Ohh okay I like how you arranged it