Question

Choose one of the factors of x^3 – 1331
x – 11

x^2 – 11x + 121

x^2 + 22x + 121

None of the above

Answer 1

Hi

Answer 2

The difference of two perfect cubes x and 11

Answer 3

yes i think that the answer would be x-11

Answer 4

Let me check:(x-11)(x^2+11x+121)

Answer 5

It is x-11 .

Answer 6

yay do you think you can help me with one more?

Answer 7

Just one lol

Answer 8

yes one more i promise.

Answer 9

go

Answer 10

Choose one of the factors of 5x3 – 135

Answer 11

its 5x^3-135

Answer 12

5(x3-27)

Answer 13

ok i got that part

Answer 14

Now notice that we x3-27 which is the difference of two perfect cubes, that can be factored further.

Answer 15

and the cubic root of 27 would be 3 right?

Answer 16

(x-3)(x2 +3x+9)(5) what are your choices? Yes

Answer 17

5

x – 3

x2 + 3x + 9

All of the above

Answer 18

What do you think is the best answer?

Answer 19

all of them

Answer 20

Bingo!

Answer 21

also can you explain how you got, (x-3)(x2 +3x+9)(5) please.

Answer 22

The difference of two cubes, is a special product that you need to memorize or know where to look.
\[(a ^{3}-b ^{3})= (a-b)(a ^{2}+ab + b ^{2)}\]

Answer 23

The sum of two cubes is also a special case and has a similar product

Answer 24

Is that a special formula to know where to plug the numbers in?

Answer 25

Yes, a was x and b was 3

Answer 26

so ok to be good with this, (a3−b3)=(a−b)(a2+ab+b2) would be substituted by
(x-3)(x^2+3x+3^2)

Answer 27

(5) at the end so if we check our work and multiply it by 5 we would get the same thing in the beginning.

Answer 28

Yes and if it was (a3+b3) it would factor to: (a+b)(a2-ab+b2)

Answer 29

alright thank you very much. I have a test tomorrow so now I'm ready.

Answer 30

Good luck on the test.

Answer 31

thanks