Finding Zeros of Polynomial Functions

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Mathematics
•
10th - 12th Grade
•
Hard
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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 n is a non-negative integer.
2.
FLASHCARD QUESTION
Front
What does it mean to find the zeros of a polynomial function?
Back
Finding the zeros of a polynomial function means determining the values of x for which the function f(x) = 0. These values are also known as the roots of the polynomial.
3.
FLASHCARD QUESTION
Front
What is the degree of a polynomial?
Back
The degree of a polynomial is the highest power of the variable in the polynomial expression. For example, in f(x) = 2x^3 - 4x + 1, the degree is 3.
4.
FLASHCARD QUESTION
Front
How many zeros can a polynomial of degree n have?
Back
A polynomial of degree n can have at most n real zeros, counting multiplicities.
5.
FLASHCARD QUESTION
Front
What is synthetic division?
Back
Synthetic division is a simplified method of dividing a polynomial by a linear factor of the form (x - c). It is faster than long division and is used to find zeros and factor polynomials.
6.
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).
7.
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).
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