Question
Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. \( x^{5}-x^{6}+x^{7}-3 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. Yes, the expression is a polynomial. The expression written in standard form is B. No, the expression is not a polynomial.
Ask by Murphy Chavez. in the United States
Mar 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression is a polynomial. In standard form, it is \( x^{7} - x^{6} + x^{5} - 3 \).
Solution
1. Identify the terms of the expression: \(x^{5}\), \(-x^{6}\), \(x^{7}\), and \(-3\).
2. Check the exponents: \(5\), \(6\), \(7\), and \(0\). Since all exponents are non-negative integers, the expression is a polynomial.
3. Write the polynomial in standard form (arranging the terms in descending order of degree):
\[
x^{7} - x^{6} + x^{5} - 3
\]
The correct choice is A.
Thus, the expression in standard form is:
\[
x^{7} - x^{6} + x^{5} - 3.
\]
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Simplify this solution The Deep Dive
A. Yes, the expression is a polynomial. The expression written in standard form is \(-x^{6} + x^{7} + x^{5} - 3\). To be a polynomial, an expression must only contain non-negative integer exponents. Although the highest exponent is negative in the order discussed, the expression contains variable terms and constants that meet the polynomial criteria.
