Topic Details (Notes format)

How to Perform Polynomial Long Division

Subject: Mathematics

Book: Maths Mastery

Polynomial long division generalizes numerical long division to algebraic expressions. Divide the highest degree term of the dividend by the highest degree term of the divisor, multiply back, and subtract, then repeat until remainder is lower degree than the divisor. For example, dividing x³+2x²–4x+1 by x–1 systematically yields a quotient x²+3x–1 and remainder 0 if (x=1) is a root. This process underpins factorization, simplifying rational expressions, and advanced calculus tasks. Mastering polynomial long division fosters skillful manipulation of polynomials in proofs and real-world models.

Practice Questions

How many ways can 4 people sit in a row?

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The simple interest on Rs. 4000 at 5% per annum for 2 years is:

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If x = 2 and y = 3, what is the value of (x^2 + y^2)?

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The area of an equilateral triangle with side length 6 cm is:

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How many diagonals does a pentagon have?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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If a number is divisible by 9, it is also divisible by which of the following?

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If a person can type 45 words per minute, how many words can they type in 2 hours?

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If x^2 + 4x + 4 = 0, what is the value of x?

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The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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