Practice Factor Theorem (8) - Polynomials - IB 10 Mathematics

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9 questions

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6 questions · about 4 min · pass mark 70%. Hints available.
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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
If P(2) = 0 for the polynomial P(x) = x^2 - 5x + 6, what can you conclude?
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Identify the root and apply the Factor Theorem.
Question 2.
For the polynomial P(x) = x - 3, what is the factor when P(3) = 0?
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Look for the value of the root.
3Question 3.
What does the Factor Theorem state?
- If P(a) = 0, then (x + a) is a factor.
- If P(a) = 0, then (x - a) is a factor.
- If P(a) ≠ 0, then (x - a) is a factor.
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Remember the condition of the polynomial when equal to zero.
4Question 4.
True or False: If x = 3 is a root of P(x), then (x - 3) cannot be a factor.
- True
- False
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Recall the definition from the Factor Theorem.
Question 5.
Given P(x) = x^4 - 4x^2 + 4, determine the complete factorization using the Factor Theorem and confirm the factors via computation.
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Apply the Factor Theorem and explore common patterns.
Question 6.
For the polynomial P(x) = x^5 - 4x^4 + 6x^3 - 24x^2, find all real factors, utilizing the Factor Theorem effectively.
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Consider grouping for suggested simplifications.

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