Answer:
The greatest common factor is 5x²
Step-by-step explanation:
Step 1 : To find the greatest common factor, break down every term of both the polynomials into prime factors
![15\cdot x^{2}\cdot y^3=3\times 5\times x\times x\times y\times y\times y\\-20\cdot x^3\cdot y\cdot z=-1\times 2\times 2\times 5\times x\times x\times x\times y\times z](https://tex.z-dn.net/?f=15%5Ccdot%20x%5E%7B2%7D%5Ccdot%20y%5E3%3D3%5Ctimes%205%5Ctimes%20x%5Ctimes%20x%5Ctimes%20y%5Ctimes%20y%5Ctimes%20y%5C%5C-20%5Ccdot%20x%5E3%5Ccdot%20y%5Ccdot%20z%3D-1%5Ctimes%202%5Ctimes%202%5Ctimes%205%5Ctimes%20x%5Ctimes%20x%5Ctimes%20x%5Ctimes%20y%5Ctimes%20z)
Step 2 : Now find the common factors which are common in both the polynomials
Common factors are : 5 , x and x
Step 3 : To find the greatest common factor find product of all the common factors obtained in the previous step
Greatest Common Factor = 5 × x × x
= 5·x²
So, The blanks will be : [5] x[2] y[0]