Question

Part 1 Create a difference of squares binomial or a perfect square trinomial that can be factored multiple times.

Part 2 Provide the factors of this polynomial.

Part 3 Explain, in complete sentences, the process you used to create the binomial/trinomial.

@texaschic101

Answer 1

@Abhisar @iPwnBunnies @sweetburger

Answer 2

Factored multiple times?
How bout something like this?\[\Large\rm x^4-16\]=o

Answer 3

oh okay I didn't seem to understand "factored multiple times part"

Answer 4

Or do they want difference of only squares, written as a binomial power?\[\Large\rm (x^2-1)^2\]

Answer 5

written as a binomial to some power*

Answer 6

That would be another option we could look at.

Answer 7

oh okay. is it possible to explain that also?

Answer 8

So the way I'm starting this is by thinking of my difference of squares formula:\[\Large\rm a^2-b^2=(a-b)(a+b)\]So I know that if I can write both numbers as perfect squares (with subtraction between them) then they'll factor nicely using this identity.\[\Large\rm x^2-1=x^2-1^2\]Factoring to,\[\Large\rm x^2-1^2=(x-1)(x+1)\]Yes?
Maybe if we stuck with the 16 it would be easier to work with.

Answer 9

Maybe I think the 16 will be easier

Answer 10

Don't you think?

Answer 11

Fine fine fine :)\[\Large\rm x^2-16 \quad=\quad x^2-4^2\]Do you understand how we could use the formula from here?

Answer 12

yes so far. :)

Answer 13

The reason I put the square on the outside of the brackets is because that's an easy way to get some factors!! c:

Remember a square tells you to multiply the `thing` by itself.

Answer 14

\[\Large\rm (x^2-16)^2=(x^2-16)(x^2-16)\]

Answer 15

oh okay would I factor that further?

Answer 16

since it's difference of two squares binomial

Answer 17

Writing 16 as 4^2 shows us that it's a perfect square.
\[\Large\rm (x^2-16)^2=(x^2-4^2)(x^2-4^2)\]

Answer 18

Then we can use our difference of squares formula on each set.\[\Large\rm =(x-4)(x+4)(x-4)(x+4)\]

Answer 19

I hope I didn't misread part 1..
The directions are a little strange :d

Answer 20

lol

Answer 21

thank you!

Answer 22

Yah I hope that made some sense to you! :o