Practice Factorization Theorem - 2.3.3 | 2. Algebra | ICSE 12 Mathematics
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Factorization Theorem

2.3.3 - Factorization Theorem

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Evaluate P(3) for the polynomial P(x) = x^2 - 5x + 6.

💡 Hint: Substitute x with 3 and simplify.

Question 2 Easy

Is (x - 1) a factor of x^2 - 3x + 2? Explain why.

💡 Hint: Check if substituting 1 makes the polynomial zero.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

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

💡 Hint: Think about what happens when substituting the root.

Question 2

True or False: If P(c) != 0, then (x - c) is a factor of the polynomial P(x).

True
False

💡 Hint: Remember the definition of factors.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Factor the polynomial P(x) = x^4 - 8x^2 + 16 completely. Identify all roots.

💡 Hint: Recognize it as a quadratic form and take square roots.

Challenge 2 Hard

For P(x) = 3x^3 - 12x^2 + 12x, find all the roots and express in factored form.

💡 Hint: Extract the common factor first, then apply the Factorization Theorem.

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