To analyze the expression $8x^3 - 2x - 5x + 7$, let's determine the appropriate descriptions for its parts.

Parts of the Expression

1. Terms are the separate components of the expression that are added or subtracted.

   • The terms in the expression are: $8x^3$, $-2x$, $-5x$, and $7$.

2. Coefficients are the numerical factors of terms containing variables.

   • The coefficients are: $8$ (from $8x^3$), $-2$ (from $-2x$), and $-5$ (from $-5x$).

3. Constants are terms that do not contain variables.

   • The constant in the expression is $7$.

Organized Mapping

• Term: $8x^3, -2x, -5x, 7$
• Coefficient: $8, -2, -5$
• Constant: $7$

Simplified Expression

If simplified, $-2x - 5x = -7x$, the expression becomes: $8x^3 - 7x + 7$

Would you like further clarification or detailed explanations? 😊

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Related Questions:

1. How do coefficients impact the degree of a polynomial?
2. What distinguishes constants from coefficients in expressions?
3. Can terms with similar variables always be combined? Why?
4. What is the degree of this polynomial, and why?
5. How can identifying terms help in factoring expressions?

Tip:

When combining like terms, ensure that the variables and their exponents match exactly!