Answer :
To find all of the coefficients in the algebraic expression [tex]\(-2x^2 + 17 - 15x + 7xy\)[/tex], we need to identify the numerical factors that multiply each term with a variable or constant:
1. Identifying Coefficients:
- Coefficient of [tex]\(x^2\)[/tex]: The term with [tex]\(x^2\)[/tex] is [tex]\(-2x^2\)[/tex]. Here, the coefficient is [tex]\(-2\)[/tex].
- Coefficient of [tex]\(x\)[/tex]: The term with [tex]\(x\)[/tex] is [tex]\(-15x\)[/tex]. Here, the coefficient is [tex]\(-15\)[/tex].
- Coefficient of [tex]\(xy\)[/tex]: The term with [tex]\(xy\)[/tex] is [tex]\(7xy\)[/tex]. Here, the coefficient is [tex]\(7\)[/tex].
- Constant term: The term that does not have a variable attached is [tex]\(17\)[/tex]. While it's not technically a coefficient of a variable, it is part of the expression as the constant term.
2. Listing Coefficients:
- The coefficients we identified are: [tex]\(-2, -15, 7\)[/tex] for the variables [tex]\(x^2\)[/tex], [tex]\(x\)[/tex], and [tex]\(xy\)[/tex], respectively, and [tex]\(17\)[/tex] as the standalone constant term.
3. In Correct Order:
- To list all the coefficients, including the constant term, we have [tex]\(-15, -2, 7, 17\)[/tex].
Thus, the final answer, which gives all the coefficients of the algebraic expression [tex]\(-2x^2 + 17 - 15x + 7xy\)[/tex], is: [tex]\(-15, -2, 7, 17\)[/tex].
1. Identifying Coefficients:
- Coefficient of [tex]\(x^2\)[/tex]: The term with [tex]\(x^2\)[/tex] is [tex]\(-2x^2\)[/tex]. Here, the coefficient is [tex]\(-2\)[/tex].
- Coefficient of [tex]\(x\)[/tex]: The term with [tex]\(x\)[/tex] is [tex]\(-15x\)[/tex]. Here, the coefficient is [tex]\(-15\)[/tex].
- Coefficient of [tex]\(xy\)[/tex]: The term with [tex]\(xy\)[/tex] is [tex]\(7xy\)[/tex]. Here, the coefficient is [tex]\(7\)[/tex].
- Constant term: The term that does not have a variable attached is [tex]\(17\)[/tex]. While it's not technically a coefficient of a variable, it is part of the expression as the constant term.
2. Listing Coefficients:
- The coefficients we identified are: [tex]\(-2, -15, 7\)[/tex] for the variables [tex]\(x^2\)[/tex], [tex]\(x\)[/tex], and [tex]\(xy\)[/tex], respectively, and [tex]\(17\)[/tex] as the standalone constant term.
3. In Correct Order:
- To list all the coefficients, including the constant term, we have [tex]\(-15, -2, 7, 17\)[/tex].
Thus, the final answer, which gives all the coefficients of the algebraic expression [tex]\(-2x^2 + 17 - 15x + 7xy\)[/tex], is: [tex]\(-15, -2, 7, 17\)[/tex].
