How to use the Remainder Theorem with Polynomials

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Mathematics, Performing Arts
•
11th Grade - University
•
Hard
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7 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a common issue when using synthetic division on polynomials with missing terms?
It always results in fractions.
It can be time-consuming.
It simplifies the process.
It requires additional steps.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
According to the Remainder Theorem, what is the remainder when a polynomial f(x) is divided by x-k?
x
f(x)
f(k)
k
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the Factor Theorem state about a polynomial if the remainder is zero?
The polynomial is undefined.
The polynomial has no real roots.
x-k is a factor of the polynomial.
The polynomial is prime.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How can you determine if x-k is a factor of a polynomial using the Factor Theorem?
By finding the derivative of the polynomial.
By checking if the remainder is zero.
By using long division.
By graphing the polynomial.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a key step when dealing with fractions in the Remainder Theorem?
Multiplying by zero.
Ignoring the fractions.
Using synthetic division.
Finding a common denominator.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why might students prefer using the Remainder Theorem over synthetic division with fractions?
It is faster.
It is more accurate.
It is less prone to errors.
It avoids complex calculations.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the remainder when evaluating f(1/2) for a polynomial using the Remainder Theorem?
1
11/8
1/2
0
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