To organize the given expressions based on the number of terms, we first need to determine how many terms are in each expression. Let's analyze each one individually:
1. Expression I: [tex]\( x + 2xyz \)[/tex]
- This expression has 2 terms: [tex]\( x \)[/tex] and [tex]\( 2xyz \)[/tex].
2. Expression II: [tex]\( 3x + y + z \)[/tex]
- This expression has 3 terms: [tex]\( 3x \)[/tex], [tex]\( y \)[/tex], and [tex]\( z \)[/tex].
3. Expression III: [tex]\( 2x^2y + x^2 - 3x + 4 \)[/tex]
- This expression has 4 terms: [tex]\( 2x^2y \)[/tex], [tex]\( x^2 \)[/tex], [tex]\( -3x \)[/tex], and [tex]\( 4 \)[/tex].
4. Expression IV: [tex]\( 9x^2yz \)[/tex]
- This expression has 1 term: [tex]\( 9x^2yz \)[/tex].
Now that we know the number of terms in each expression, we can arrange them from greatest to least:
- Expression III has 4 terms.
- Expression II has 3 terms.
- Expression I has 2 terms.
- Expression IV has 1 term.
So, the order from greatest to least number of terms is:
III, II, I, IV
Thus, the correct answer is the first option:
III, II, I, IV
