Remainder theorem/Factor theorem
Flashcard
•
Mathematics
•
11th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the Remainder Theorem?
Back
The Remainder Theorem states that if a polynomial f(x) is divided by (x - c), the remainder of this division is f(c).
2.
FLASHCARD QUESTION
Front
What is the Factor Theorem?
Back
The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.
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
Evaluate f(3) for f(x) = 3x^3 + 10x^2 - x - 12.
Back
f(3) = 3(3)^3 + 10(3)^2 - (3) - 12 = 81 + 90 - 3 - 12 = 156.
5.
FLASHCARD QUESTION
Front
Is (x - 3) a factor of f(x) = 3x^3 + 10x^2 - x - 12?
Back
No, it is not a factor because f(3) ≠ 0.
6.
FLASHCARD QUESTION
Front
Evaluate f(4) for f(x) = x^3 + x^2 - 16x - 16.
Back
f(4) = (4)^3 + (4)^2 - 16(4) - 16 = 64 + 16 - 64 - 16 = 0.
7.
FLASHCARD QUESTION
Front
Is (x - 4) a factor of f(x) = x^3 + x^2 - 16x - 16?
Back
Yes, it is a factor because f(4) = 0.
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