Practice Division Of Polynomials Over Fields (20.1) - Polynomials Over Fields and Properties

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9 questions

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6 sample questions

Question 1.
Provide an example of a polynomial and find its division with another polynomial.
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Use polynomial long division.
Question 2.
What is the degree of the polynomial 4x^3 - 2x + 7?
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Look for the highest exponent.
3Question 3.
What is polynomial division?
- Finding area under a curve
- Dividing one polynomial by another to find quotient and remainder
- Adding two polynomials
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Think about how division works in arithmetic.
4Question 4.
True or False: All polynomials can be factored into irreducible polynomials.
- True
- False
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Consider the factorization theorem.
Question 5.
Find the GCD of the polynomials 3x^2 - 3x + 1 and 2x^2 + x - 1. Show your work.
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Remember to apply the division step repeatedly.
Question 6.
Prove that x^2 + 2x + 1 is reducible and express it in factored form.
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Use the method of completing the square or recognize it as a perfect square trinomial.

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