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.

Answer 1

1. x^2 - 9
2. (x-3)(x+3)
3. Begin with two linear functions, f(x) = x - 3 and g(x) = x + 3. Then, multiply them by each other to get the expression (x-3)(x+3). Finally expand the expression to get x^2 - 9.

Answer 2

Am I mistaken? Anyone?

Answer 3

can it be factored multiple times?

Answer 4

It can be factored n times. \[\tiny{\text{where n = 1}}\]

Answer 5

Right. if you want one that can be factored multiple times, there's a way

x^4 - 1 = (x^2 - 1)(x^2 + 1)
= (x-1)(x+1)(x^2+1)

Answer 6

the way to create that is by beginning with an ordinary difference of squares binomial like (x^2 - 1), and then substituting x by x^2 so that you get x^4 - 1

Answer 7

give me one that can be factored multiple times, and do the part 1 and 2 and 3 to that.. cause it says multiple times

Answer 8

I would start with the factors just like agdgdgdgwngo did.
Maybe use (x+1)(x-1)(x+2)(x-2) and then factor it out to get the polynomial...

Answer 9

lol so confusing !!!

Answer 10

that's it; x^4 - 1 is a binomial that may be factored multiple times.