Polynomial Functions & Equations

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•
Mathematics
•
9th - 12th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a polynomial function?
Back
A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is: f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n ≠ 0.
2.
FLASHCARD QUESTION
Front
What does it mean for a number to be a zero of a polynomial?
Back
A zero of a polynomial is a value of x that makes the polynomial equal to zero. In other words, if f(x) = 0, then x is a zero of the polynomial.
3.
FLASHCARD QUESTION
Front
What is the Factor Theorem?
Back
The Factor Theorem states that if f(c) = 0 for a polynomial f(x), then (x - c) is a factor of f(x).
4.
FLASHCARD QUESTION
Front
What is the Remainder Theorem?
Back
The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder of that division is f(c).
5.
FLASHCARD QUESTION
Front
How do you find the zeros of a polynomial function?
Back
To find the zeros of a polynomial function, set the function equal to zero and solve for x. This may involve factoring, using the quadratic formula, or other algebraic methods.
6.
FLASHCARD QUESTION
Front
What is the multiplicity of a zero?
Back
The multiplicity of a zero refers to the number of times a particular zero appears as a root of the polynomial. A zero with an even multiplicity will touch the x-axis, while a zero with an odd multiplicity will cross the x-axis.
7.
FLASHCARD QUESTION
Front
What is synthetic division?
Back
Synthetic division is a simplified method of dividing a polynomial by a linear divisor of the form (x - c). It is faster than long division and is used to find the quotient and remainder.
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