Practice Rational Root Theorem (4.1) - Cubic Functions - IB 10 Mathematics – Group 5, Algebra

Practice: Rational Root Theorem

Lesson 4.1Cubic Functions

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8 questions

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6 sample questions

Question 1.
List the possible rational roots for the polynomial $f(x) = x^3 - 4x^2 + 4x - 1$ .
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Use the factors of -1 divided by the factors of 1.
Question 2.
Identify the factors of 3.
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Consider numbers that can multiply to give 3.
3Question 3.
What does the Rational Root Theorem help you determine?
- The degree of the polynomial
- Possible rational roots
- Complex roots
- End behavior of graphs
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Think about what we can find using factors.
4Question 4.
True or False: The Rational Root Theorem can only find integer roots.
- True
- False
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Consider the structure of rational numbers.
Question 5.
For the cubic polynomial $f(x) = 5x^3 - 4x^2 + 3x - 2$ , find all possible rational roots, and confirm any that work using synthetic division.
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Factorize -2 and 5 for potential roots.
Question 6.
Using the Rational Root Theorem, find possible rational roots for $f(x) = 6x^3 + x^2 - 8x - 4$ , and explain how to confirm them.
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Focus on factors of 4 and 6.

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