Topic Details (Notes format)

How to Use Remainder Theorems (Polynomial Division)

Subject: Mathematics

Book: Maths Mastery

The Remainder Theorem states that the remainder when a polynomial f(x) is divided by (x – a) is simply f(a). For example, if you want the remainder when x² – 5x + 6 is divided by (x – 3), evaluate f(3) = 3² – 5×3 + 6 = 9 – 15 + 6 = 0. The Factor Theorem extends this, indicating if f(a) = 0, then (x – a) is a factor of the polynomial. These shortcuts alleviate long division and facilitate polynomial factoring, essential in solving polynomial equations, analyzing algebraic structures, and simplifying advanced math problems with speed and precision.

Practice Questions

A man invests Rs. 5000 at 5% per annum simple interest. What is the total amount after 3 years?

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If x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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What is the greatest common divisor (GCD) of 36 and 48?

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If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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

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What is the square root of 121?

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