To determine the number of terms in the algebraic expression [tex]\( 2y + 3x - 5x^2 - 9 \)[/tex], we need to identify each separate term within the expression.
A term in an algebraic expression is any individual component that is separated by a plus (+) or minus (-) sign.
Let's break down the given expression:
1. [tex]\( 2y \)[/tex] is a term.
2. [tex]\( 3x \)[/tex] is another term.
3. [tex]\( -5x^2 \)[/tex] is a term (the minus sign indicates it's a negative term).
4. [tex]\( -9 \)[/tex] is also a term (even though it is a constant, it still counts as a term).
So, when we list out all the terms we have:
- [tex]\( 2y \)[/tex]
- [tex]\( 3x \)[/tex]
- [tex]\( -5x^2 \)[/tex]
- [tex]\( -9 \)[/tex]
Counting these, we see there are 4 distinct terms in the algebraic expression.
Therefore, the number of terms in the expression [tex]\( 2y + 3x - 5x^2 - 9 \)[/tex] is [tex]\( 4 \)[/tex].
The correct answer is:
4
