Division algorithm for polynomials
For polynomials p(x) and g(x), with g(x) not equal to zero, p(x)=g(x)q(x)+r(x), where the degree of r(x) is less than the degree of g(x).
Practice This ConceptMain explanation
Teacher explanation
The division algorithm is the polynomial version of ordinary division. It tells us that dividend = divisor × quotient + remainder. This idea is useful for dividing one polynomial by another, checking factors, and finding remainders. Students should remember the rule about the degree of the remainder, because that is often asked in theory questions.
Example
If p(x)=x^2-1 and g(x)=x-1, then p(x)=(x-1)(x+1)+0.
Simple analogy
Dividend = divisor × quotient + remainder.
Common confusion
Students sometimes write a remainder whose degree is equal to or greater than the divisor. That is not allowed.
Exam tip
Always check that the remainder has lower degree than the divisor before finalising the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of division algorithm for polynomials in one clean line.
2-mark use
Define division algorithm for polynomials and add one example or condition.
3-mark use
Explain division algorithm for polynomials, show the method or example, and mention the common mistake.
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Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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