A2 - Factor and Remainder Theorem
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the Factor Theorem?
Back
The Factor Theorem states that a polynomial f(x) has a factor (x - c) if and only if f(c) = 0.
2.
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 is f(c).
3.
FLASHCARD QUESTION
Front
How do you perform synthetic division?
Back
Synthetic division is a simplified form of polynomial long division. It involves using the coefficients of the polynomial and the zero of the divisor.
4.
FLASHCARD QUESTION
Front
What is a zero of a polynomial?
Back
A zero of a polynomial is a value of x that makes the polynomial equal to zero.
5.
FLASHCARD QUESTION
Front
If f(x) = 2x^3 + 3x^2 - 5, what is f(1)?
Back
f(1) = 2(1)^3 + 3(1)^2 - 5 = 0.
6.
FLASHCARD QUESTION
Front
What does it mean for (x - 3) to be a factor of a polynomial?
Back
It means that when the polynomial is divided by (x - 3), the remainder is zero.
7.
FLASHCARD QUESTION
Front
How can you find all factors of a polynomial?
Back
You can find all factors by using synthetic division, the Factor Theorem, and testing possible rational roots.
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