Practice Factorization Theorem (2.3.3) - Algebra

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

Question 1.
Evaluate P(3) for the polynomial P(x) = x^2 - 5x + 6.
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Substitute x with 3 and simplify.
Question 2.
Is (x - 1) a factor of x^2 - 3x + 2? Explain why.
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Check if substituting 1 makes the polynomial zero.
3Question 3.
What does the Factorization Theorem state?
- If P(x) is a polynomial, then it has a root
- If a linear factor exists, the polynomial equals zero at that point
- It states nothing about roots
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Think about what happens when substituting the root.
4Question 4.
True or False: If P(c) != 0, then (x - c) is a factor of the polynomial P(x).
- True
- False
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Remember the definition of factors.
Question 5.
Factor the polynomial P(x) = x^4 - 8x^2 + 16 completely. Identify all roots.
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Recognize it as a quadratic form and take square roots.
Question 6.
For P(x) = 3x^3 - 12x^2 + 12x, find all the roots and express in factored form.
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Extract the common factor first, then apply the Factorization Theorem.

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