Factorisation

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Factorisation is the process of writing an expression as a product of its factors. It is the reverse of multiplication. Example: x² + 5x + 6 = (x + 3)(x + 2), where (x + 3) and (x + 2) are factors of

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The first step is to look for common factors. Find the H.C.F. (Highest Common Factor) of all terms and take it out as a common factor. Example: 6a² - 3ax = 3a(2a - x), where 3a is the common factor.

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Step 1: Find H.C.F. of 8ab² and 12a²b = 4ab Step 2: 8ab² + 12a²b = 4ab(2b + 3a) Answer: 4ab(2b + 3a)

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The grouping method is used when an expression has an even number of terms that can be arranged in groups where each group has a common factor. Steps: 1) Group terms appropriately 2) Factor each group

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Step 1: Group terms: (ab + bc) + (ax + cx) Step 2: Factor each group: b(a + c) + x(a + c) Step 3: Take common factor: (a + c)(b + x) Answer: (a + c)(b + x)

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A trinomial is a polynomial with three terms. The general form is ax² + bx + c, where 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term. Example: 2x² + 5x + 3

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Step 1: Find two numbers whose sum = b and product = ac Step 2: Split the middle term using these numbers Step 3: Group and factorise Example: x² + 5x + 6 = x² + 3x + 2x + 6 = x(x+3) + 2(x+3) = (x+3)(

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Need two numbers with sum = -5 and product = 6 These are -3 and -2 (since -3 + (-2) = -5 and (-3) × (-2) = 6) x² - 5x + 6 = x² - 3x - 2x + 6 = x(x-3) - 2(x-3) = (x-3)(x-2)