A2 - Factor and Remainder Theorem

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•
Mathematics
•
9th - 12th Grade
•
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 of this division is f(c).
3.
FLASHCARD QUESTION
Front
How do you determine if (x - c) is a factor of f(x)?
Back
To determine if (x - c) is a factor of f(x), evaluate f(c). If f(c) = 0, then (x - c) is a factor.
4.
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).
5.
FLASHCARD QUESTION
Front
How do you use synthetic division to evaluate f(c)?
Back
To evaluate f(c) using synthetic division, set up the synthetic division with c and the coefficients of f(x). The remainder will be f(c).
6.
FLASHCARD QUESTION
Front
What is a zero of a polynomial function?
Back
A zero of a polynomial function f(x) is a value of x for which f(x) = 0.
7.
FLASHCARD QUESTION
Front
How can you find the real zeros of a polynomial?
Back
To find the real zeros of a polynomial, factor the polynomial and set each factor equal to zero, then solve for x.
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