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 the product of two numbers is 120 and their sum is 26, what are the numbers?

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If the sum of the squares of two consecutive positive integers is 365, 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 x:y = 4:5 and y:z = 2:3, what is x:z?

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

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A triangle has angles 60°, 60°, and 60°. What type of triangle is it?

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A train 150 m long passes a pole in 15 seconds. What is its speed?

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If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

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What is the area of a circle with a diameter of 14 cm?

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