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

The LCM of 12 and 15 is:

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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 sum of all even numbers between 1 and 50?

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

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If 2x - 3 = 7, what is the value of x?

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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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What is the HCF of 72 and 120?

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The probability of getting an even number when rolling a die is:

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A number is increased by 20% and then decreased by 20%. What is the net change?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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