Practice Remainder Theorem - 2.3.2 | 2. Algebra | ICSE 12 Mathematics
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Remainder Theorem

2.3.2 - Remainder Theorem

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Practice Questions

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Question 1 Easy

What is the remainder when \(P(x) = x^2 + x - 6\) is divided by \(x - 3\)?

💡 Hint: Use the Remainder Theorem and substitute \\(x = 3\\).

Question 2 Easy

Calculate the remainder when \(P(x) = x^3 + 2x + 1\) is divided by \(x + 1\).

💡 Hint: Evaluate at \\(x = -1\\).

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the Remainder Theorem help to calculate?

Remainder of polynomial division
Sum of polynomial terms
Degree of a polynomial

💡 Hint: Think about what the theorem states regarding division.

Question 2

T/F: The remainder can be found by substituting the linear divisor's root into the polynomial.

True
False

💡 Hint: Recall the theorem's statement about division.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove that if \(P(x) = x^4 - 5x^3 + 6x^2\) has a remainder of \(0\) when divided by \(x - 3\), that \(x - 3\) is a factor.

💡 Hint: Don't forget to substitute \\(3\\) into \\(P(x)\\).

Challenge 2 Hard

Given \(P(x) \) is divided by \(x - 1\), find \(P(x)\) for it to yield a remainder of \(4\). Write a polynomial.

💡 Hint: Incorporate any polynomial as \\(Q(x)\\) such that this holds true.

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