Question

Factor:
c^3+64

Answer 1

See factoring pattern on attachment.

Answer 2

c^3+64 is the sum of two cubes.

c³ + 4³

Answer 3

c³ + 4³ = (c + 4) ( ? - ? + ? )

Answer 4

(c^2-4c+16)

Answer 5

Yes.

c³ + 4³ = (c + 4)* (c^2-4c+16)

Answer 6

Can you help my factor this?
\[z^4-21z^2\]

Answer 7

Factor out the largest common factor of z².

z² ( ? - ?)

Answer 8

(z^2-7)?

Answer 9

z^4 - 21 z^2 = z² (z² - 21) is what I got.

Answer 10

Yours multiplies back to z^4 - 7 z^2 which is not the original problem.

Answer 11

Oh i see now. thank you! :D

Answer 12

I think it is a good idea to check the factoring, especially the monomial ones, by multiplying back.

Answer 13

Do you have another problem?

Answer 14

yes.

Answer 15

Factor out the GCF
x+6+3a(x+6)

Answer 16

This is factoring by grouping.

Answer 17

x+6+3a(x+6) =

1* (x + 6) + 3a * ( x + 6 )

Answer 18

( x + 6 ) is the common factor.

Answer 19

so it would be (3a+1)(x+6)?

Answer 20

It is like having 6x + 6y and factoring out the common factor of 6.

But, the common factor is a binomial this time.

Answer 21

1* (x + 6) + 3a * ( x + 6 ) = ( x + 6 ) * ( 1 + 3a) which is the same answer you got.

Answer 22

Next question :)

Answer 23

t^2+10ty+16y^2

Answer 24

I don't see any common monomial factors.

Answer 25

so that would make it Prime right?

Answer 26

It is not prime.

Answer 27

1*t^2 + 10ty + 16 y^2

We will work this by grouping.

What are two numbers that multiply to 1*16 and add to 10?

Answer 28

8,2 ?

Answer 29

Correct.

Answer 30

(t+8y)(t+2y)?

Answer 31

1*t^2 + 10ty + 16 y^2 = t^2 + 8 ty + 2 ty + 16y^2.

Answer 32

Yes, that is correct.

Answer 33

Great! :D thank you so much! :D

Answer 34

I am going to make up a problem for you to tackle. Hold on.

Answer 35

Factor 12x^2+16x-35

Answer 36

find the gcf first right?

Answer 37

Look for one, yes.

Answer 38

i can't find one.

Answer 39

Look for two numbers that multiply to (12)*(-35) AND add to 16. This expression will factor.

Answer 40

(6x-7)(2x+5)

Answer 41

I was looking a prime factors of 12 and 35.

How did you get this: (6x-7)(2x+5)

Answer 42

6*2 =12 giving 12x^2
6*5=30
-7*2=-14
-7*5=-35

12x^2+30x-14x-35
=12x^2+16-35

Answer 43

Correct. You are showing that the factorization is correct.

The more factoring problems on which you practice, the better you will get.

Consider cranking out the problems on the site http://library.thinkquest.org/29292/quadratic/2factoring/practice.htm

The answers are on the second page.

Answer 44

How about this problem:

Factor: (x^2 - 1) - ( -1 - x)

Answer 45

This is factoring by grouping.

Answer 46

(x^2 - 1) - 1* ( -1 - x) = (x^2 - 1) + 1 + x.

Use the distributive property to multiply the "understood" -1 by (-1 - x)

Answer 47

= (x^2 - 1) + (1 + x).

What do you know about the factorization of this: (x^2 - 1)