+2446 What is \(\frac{0}{0}\)?
Mathematicians are not actually debating the answer to this. It is well-known that it is undefined. 0/0 always contradicts itself--no matter what angle you try to get its value from.
Let's see what happens if both the numerator and denominator both try o get equally close to 0
| Tries | Result | ||
| \(\frac{0.1}{0.1}\) | \(1\) | ||
| \(\frac{0.01}{0.01}\) | \(1\) | ||
| \(\frac{0.0001}{0.0001}\) | \(1\) | ||
| \(\frac{1*10^{-90}}{1*10^{-90}}\) | \(1\) |
What happens if we try to make the denominator closer to zero while remaining the numerator as 0.
| Try | Result | |
| \(\frac{0}{1}\) | \(0\) | |
| \(\frac{0}{0.1}\) | \(0\) | |
| \(\frac{0}{0.000001}\) | \(0\) | |
| \(\frac{0}{0.000000000000000000000000000000000000000000001}\) | \(0\) | |
| \(\frac{0}{1*10^{-10000000}}\) | \(0\) | |
Both of these suggest that 0 tends toward 2 different values, which is a contradiction. Thus, 0/0 is undefined.
+2446 I'm assuming that you want to factor this. The only thing we can do is factor out a GCF. This cannot be represented as a product of two binomials.
| \(15y^3z^3-27y^2z^4+3yz^3\) | Factor out the GCF, which is 3yz^3. |
| \(3yz^3(5y^2-9yz+1)\) | The second term has 2 variables in it, which indicates that this trinomial is irreducible. |
