Final answer:
The expressions are broken down into their parts: terms, coefficients, constants, and degree. Expression 1 has terms 18x³y², 8x², -32y, -6, with coefficients 18, 8, -32, a constant -6, and degree 5. Expression 2 has terms 9x´y³, -2x³, 6y, 3, with coefficients 9, -2, 6, a constant 3, and degree 7.
Step-by-step explanation:
When identifying the parts of each polynomial expression, we look for terms, coefficients, constants, and degree.
- The terms of a polynomial are the separate elements that are added or subtracted within the expression.
- The coefficient is the numerical factor in front of variables within a term.
- A constant is a term without a variable, meaning it does not change.
- The degree of the polynomial is the highest degree of any term when you add the exponents of the variables within that term.
For expression 1: 18x³y² + 8x² – 32y – 6 we have:
- Terms: 18x³y², 8x², -32y, -6
- Coefficients: 18, 8, -32
- Constants: -6
- Degree: 5 (from the term 18x³y² since 3+2=5)
For expression 2: 9x´y³ – 2x³ + 6y + 3 we have:
- Terms: 9x´y³, -2x³, 6y, 3
- Coefficients: 9, -2, 6
- Constants: 3
- Degree: 7 (from the term 9x´y³ since 4+3=7)
Remember, when graphing polynomials, the shape of the curve changes as the constants are adjusted, and each term contributes to the overall shape of the curve.