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Identify the parts of each expression: terms, coefficients, constants, and degree.

1. 18x³ y² + 8x² – 32y - 6
2. 9x⁴y³– 2x³ + 6y + 3

User Ohlr
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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.

User Arpo
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