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

If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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What is the remainder when 5^100 is divided by 3?

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If the sum of three consecutive integers is 72, what are the integers?

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A man spends 75% of his income and saves Rs. 600. What is his total income?

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The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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What is the area of an equilateral triangle with side length 10 cm?

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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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What is the value of x if 3x + 7 = 16?

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If x - y = 5 and x + y = 15, what is the value of x?

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The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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