The function -12 - 8x^2 + 5x - 21x^7 is a polynomial. True or False

True.

The function \(-12 - 8x^2 + 5x - 21x^7\) is indeed a polynomial. A polynomial is an expression consisting of variables (in this case, \(x\)) raised to non-negative integer powers, multiplied by coefficients, and combined using addition, subtraction, or multiplication. In this expression:

- \(-12\) is a constant term.
- \(-8x^2\) has a variable \(x\) raised to the power of 2.
- \(5x\) has a variable \(x\) raised to the power of 1.
- \(-21x^7\) has a variable \(x\) raised to the power of 7.

All exponents are non-negative integers, so this is a polynomial.

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Here are 5 related questions:

1. What is the degree of the polynomial \(-12 - 8x^2 + 5x - 21x^7\)?
2. How do you classify polynomials based on their degree?
3. What is the leading coefficient of the polynomial \(-12 - 8x^2 + 5x - 21x^7\)?
4. Can you identify the constant term in the polynomial \(-12 - 8x^2 + 5x - 21x^7\)?
5. How do you add or subtract two polynomials?

**Tip:** When analyzing polynomials, always check the exponents of the variable to ensure they are non-negative integers.

Explore whether the function -12 - 8x^2 + 5x - 21x^7 qualifies as a polynomial. Understand the definition of polynomials, their components including constant terms and variable powers, and their classification based on the form. Suitable for students and learners interested in algebraic expressions.

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