Final answer:
The expression that is not a polynomial is a) √7x³ + 323 − 8, as it contains a square root of a term involving a variable which is not permitted in polynomial expressions. The correct answer is option A.
Step-by-step explanation:
A polynomial is a mathematical expression that contains two or more algebraic terms that are added, subtracted, or multiplied (no division allowed!). Polynomial expressions include at least one variable and typically include constants and positive exponents as well.
The student has inquired which expression is not considered a polynomial. We can approach this by examining each option.
- a) √7x³ + 323 − 8: This expression is not a polynomial because of the square root of a term involving a variable. A polynomial consists of a sum of terms where each term is a product of a constant and a non-negative integer power of variables. Square roots are not allowed in polynomial terms.
- b) 172x² + x − 3: This expression is a second-degree polynomial in the standard form at² + bt + c = 0, where the variables are raised to non-negative integer powers.
- c) 0: The constant zero is considered a polynomial of degree zero.
- d) 4x⁴ − x² + 5: This expression is a polynomial as well, with the highest power being four, making it a fourth-degree polynomial.
Thus, the expression that is not a polynomial is a) √7x³ + 323 − 8.