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

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If 2a + b = 10 and a - b = 4, what is the value of a?

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What is the length of the diagonal of a square with a side length of 7 cm?

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The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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What is the cube of 4?

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

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