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 = 2 and b = 3, what is the value of (a^2 + b^2)?

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The area of an equilateral triangle with side length 6 cm is:

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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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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What is the sum of all angles in a hexagon?

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What is the square root of 0.25?

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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 2x = 16, what is the value of x?

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What is the value of log₃(27)?

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