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$4x^3 + 7x^2 + 12$ is $O(x^3)$

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Factor sums and differences of cubes

Full solution

Q.

4x^3 + 7x^2 + 12

is

O(x^3)

Identify Highest Degree Term: We need to find the highest degree term in the polynomial because that's what determines the big O notation. $\newline$ Calculation: The highest degree term is $4x^3$ .
Calculate Big O Notation: Since $4x^3$ is the term with the highest degree, the big O notation is based on this term. $\newline$ Calculation: $O(x^3)$ is the big O notation for the function.

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