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Standard form of a polynomial

Check the final answer first, then review the worked steps.

Problem

Standard form of a polynomial

Answer

\(3x^2 + 10x - 8\)

Step-by-step solution

  1. Identify the terms: The given polynomial is $10x + 3x^2 - 8$. The terms are $10x$, $3x^2$, and $-8$.
  2. Determine the degree of each term: The degree of a term is the exponent of the variable. The degree of $10x$ is 1 (since $x = x^1$). The degree of $3x^2$ is 2. The degree of $-8$ is 0 (since it's a constant term).
  3. Order the terms by degree in descending order: The standard form of a polynomial arranges the terms from the highest degree to the lowest degree. So, we order the terms as $3x^2$, $10x$, and $-8$.
  4. Write the polynomial in standard form: Combining the ordered terms, we get $3x^2 + 10x - 8$.