Sure! Let's identify the constant term in the given algebraic expression [tex]\(-2 x^2 + 17 - 15 x + 7 x y\)[/tex].
1. Understand the Structure of the Expression:
The algebraic expression contains multiple terms, each potentially containing variables (like [tex]\(x\)[/tex] and [tex]\(y\)[/tex]) and constants.
2. Identify the Constant Term:
The constant term is the part of the expression that does not change with respect to the variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. It is not multiplied by any variable.
- [tex]\( -2x^2 \)[/tex]: This term contains the variable [tex]\(x\)[/tex] and hence is not a constant.
- [tex]\( 17 \)[/tex]: This term does not contain any variable. So, it is a constant term.
- [tex]\( -15x \)[/tex]: This term contains the variable [tex]\(x\)[/tex] and hence is not a constant.
- [tex]\( 7xy \)[/tex]: This term contains variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex] and hence is not a constant.
3. Conclusion:
The constant term in the algebraic expression [tex]\(-2 x^2 + 17 - 15 x + 7 x y\)[/tex] is 17.
So, the constant term is:
[tex]\[ \boxed{17} \][/tex]
