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

What is the slope of a line passing through the points (2, 3) and (4, 7)?

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If x = 3 and y = 4, what is the value of x^2 + y^2?

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What is the square root of 121?

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If a number is divisible by 9, it is also divisible by which of the following?

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

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

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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If a cylinder has a radius of 7 cm and height of 10 cm, what is its volume?

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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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