
Polynomial Divisibility and Induction

Interactive Video
•
Mathematics
•
9th - 10th Grade
•
Hard

Aiden Montgomery
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main difference between numerical and polynomial division in the context of divisibility proofs?
Numerical division deals with numbers, while polynomial division deals with functions.
Numerical division is easier than polynomial division.
Polynomial division is only applicable to linear functions.
Numerical division requires a calculator.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in the induction process for proving divisibility?
Factorize the polynomial.
Use the remainder theorem.
Test the base case, usually n=2.
Assume the statement is true for n=k.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the context of polynomial divisibility, what does the factorization of x^2 - 1 demonstrate?
That x^2 - 1 is equal to x + 1.
That x^2 - 1 cannot be factorized.
That x^2 - 1 is divisible by x - 1.
That x^2 - 1 is a prime polynomial.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of making assumptions in the induction process?
To simplify the polynomial.
To find the roots of the polynomial.
To express the polynomial in a form that includes a common factor.
To eliminate the need for further proof.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the proof by induction, what is the significance of expressing x^k+1 as x times x^k?
It shows that x^k+1 is not divisible by x - 1.
It proves that x^k+1 is a prime polynomial.
It helps in identifying the common factor x - 1.
It simplifies the polynomial to a constant.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is it important to balance the equation by adding x after subtracting it?
To eliminate the x term completely.
To make the polynomial a constant.
To ensure the equation remains valid.
To convert the polynomial into a linear function.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What emerges as a common factor in the proof by induction?
x^k
x - 1
x^2
x + 1
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