Polynomial Operations and End Behavior
Master key concepts of polynomial degree, leading coefficients, arithmetic operations, and predicting long-run behavior.
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Questions Covered in This Set
10 cards to master
What is the degree of a polynomial?
The highest power of the variable in the polynomial expression.
What is the leading coefficient?
The coefficient of the term with the highest degree in a polynomial.
How do you add or subtract polynomials?
Combine like terms—terms with the same variable and exponent.
When multiplying two polynomials, how do you find the degree of the product?
Add the degrees of the two polynomials being multiplied.
What determines a polynomial's end behavior?
The degree (even or odd) and the sign of the leading coefficient.
End behavior for even degree with positive leading coefficient?
Both ends rise: as x approaches ±∞, f(x) approaches +∞.
End behavior for odd degree with negative leading coefficient?
Left side rises, right side falls: as x→-∞, f(x)→+∞; as x→+∞, f(x)→-∞.
Why does the highest-degree term dominate end behavior?
For large |x|, the highest-degree term grows much faster than lower-degree terms, making them negligible.
What is a constant term in a polynomial?
The term without a variable, representing the y-intercept of the polynomial function.
Maximum number of turning points for a degree 5 polynomial?
Four turning points, which is one less than the degree of the polynomial.
