Q1
What does the Remainder Theorem state?
ARemainder of p(x)÷(x-a) equals p(a)
BRemainder is always zero
Cp(x) has no remainder ever
DNothing specific
ICSEClass 10 (ICSE)MathematicsCh 8 · Topic 1
Remainder and Factor Theorems
The Remainder Theorem finds the remainder when dividing a polynomial by a linear factor, while the Factor Theorem determines if a value is a
Core concept
The Remainder Theorem states that when a polynomial p(x) is divided by (x-a), the remainder equals p(a).
How it works
The Factor Theorem states that (x-a) is a factor of p(x) if and only if p(a) = 0.
Why it matters
These theorems help us find factors of polynomials without performing long division, making factorisation more efficient.
Key detail
Understanding these theorems is essential for factorising higher-degree polynomials and solving related algebraic equations.
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• Remainder Theorem: dividing p(x) by (x-a), remainder = p(a).
• Factor Theorem: (x-a) is a factor if p(a)=0.
• These avoid long division for finding factors.
• They make factorisation more efficient.
• Used for higher-degree polynomials.
• They help solve related algebraic equations.
• Both theorems are related concepts.
• Practice builds polynomial factorisation skills.