find three factorizations for the monomial 72x^8

72x^8 is 12x^4 * ?

72x^8

= (36)(2)x^8
or
= (12)(6)(x^3)(x^5)

or
.... , your turn

To find three factorizations for the monomial 72x^8, we need to find two factors that multiply together to give us 72x^8.

Factorization 1:
We can divide the monomial by 12x^4 to get the first factor. So, the first factor is 12x^4.
To find the second factor, we divide 72x^8 by 12x^4:
(72x^8) / (12x^4) = 6x^(8-4) = 6x^4.
Therefore, the second factor is 6x^4.

Factorization 1: 12x^4 * 6x^4

Factorization 2:
Another factorization for 72x^8 can be found by dividing the monomial by 6x^4 to get the first factor:
72x^8 / 6x^4 = 12x^(8-4) = 12x^4.
So, the first factor is 12x^4.
To find the second factor, we divide 72x^8 by 12x^4:
(72x^8) / (12x^4) = 6x^(8-4) = 6x^4.
Hence, the second factor is 6x^4.

Factorization 2: 12x^4 * 6x^4

Factorization 3:
A third factorization can be found by dividing 72x^8 by a different number or variable. For example, we can divide it by 3x^2 to get the first factor:
72x^8 / 3x^2 = 24x^(8-2) = 24x^6.
Therefore, the first factor is 24x^6.
To find the second factor, we divide 72x^8 by 24x^6:
(72x^8) / (24x^6) = 3x^(8-6) = 3x^2.
Thus, the second factor is 3x^2.

Factorization 3: 24x^6 * 3x^2

So, three factorizations for the monomial 72x^8 are:
1) 12x^4 * 6x^4
2) 12x^4 * 6x^4
3) 24x^6 * 3x^2