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 the radius of a circle is doubled, what happens to its area?

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

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

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If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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

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If 3x = 81, what is the value of x?

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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

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

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