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

If sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?

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The ratio of two numbers is 3:5, and their sum is 64. What are the numbers?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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If x = 3 and y = 4, what is the value of x^2 + y^2?

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

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If the sum of three consecutive integers is 96, what are the integers?

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If the perimeter of a square is 36 cm, what is the length of its diagonal?

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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

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A cube has a side length of 4 cm. What is its volume?

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