What is synthetic division?
Synthetic Division Review

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•
Mathematics
•
12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c). It is faster than long division and is used primarily for polynomials.
2.
FLASHCARD QUESTION
Front
What does it mean if the remainder is zero in synthetic division?
Back
If the remainder is zero, it indicates that the linear binomial (x - c) is a factor of the polynomial.
3.
FLASHCARD QUESTION
Front
How do you determine the remainder when dividing a polynomial by (x - c)?
Back
To find the remainder, substitute c into the polynomial. The result is the remainder.
4.
FLASHCARD QUESTION
Front
What is the significance of using a zero placeholder in synthetic division?
Back
A zero placeholder is used to represent missing terms in the polynomial, ensuring that the degrees of the terms align correctly during the division process.
5.
FLASHCARD QUESTION
Front
If f(x) = x^3 - 4x + 1, what is f(2)?
Back
f(2) = 2^3 - 4(2) + 1 = 8 - 8 + 1 = 1.
6.
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.
7.
FLASHCARD QUESTION
Front
What is the relationship between synthetic division and the Remainder Theorem?
Back
The Remainder Theorem states that the remainder of the division of f(x) by (x - c) is f(c). Synthetic division is a method to compute this remainder.
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