
PreCalculus Flashcard Review - Chapter 2 (Sections 2.1 - 2.4)
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the Rational Root Theorem?
Back
The Rational Root Theorem states that any rational solution (or root) of a polynomial equation, in the form of a fraction p/q, must have p as a factor of the constant term and q as a factor of the leading coefficient.
2.
FLASHCARD QUESTION
Front
How do you find the remainder of a polynomial when divided by a linear factor?
Back
Use the Remainder Theorem, which states that the remainder of the division of a polynomial P(x) by (x - c) is P(c).
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.
4.
FLASHCARD QUESTION
Front
How many roots can a polynomial of degree n have?
Back
A polynomial of degree n can have at most n roots.
5.
FLASHCARD QUESTION
Front
What is synthetic division?
Back
Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor of the form (x - c).
6.
FLASHCARD QUESTION
Front
What is the significance of the leading coefficient in a polynomial?
Back
The leading coefficient determines the end behavior of the polynomial function as x approaches positive or negative infinity.
7.
FLASHCARD QUESTION
Front
What are the possible rational zeros of the polynomial f(x) = 2x^3 - 3x^2 + 4?
Back
The possible rational zeros can be found using the Rational Root Theorem, which suggests testing factors of the constant term (4) over factors of the leading coefficient (2). Possible rational zeros are ±1, ±2, ±4, ±1/2.
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