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

The LCM of 12 and 15 is:

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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What is the sum of all even numbers between 1 and 100?

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

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What is the value of x if log(x) + log(4) = log(32)?

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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 the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

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The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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What is the sum of all odd numbers from 1 to 99?

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If sin(θ) = 0.6 and θ is acute, what is cos(θ)?

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