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Factorisation of Quadratic Polynomials- Middle Term Splitting

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Question

Factorise: $x^{2} + 12 x + 35 = 0$

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Solution

$\begin{matrix} L e t x^{2} + 12 x + 35 = p (x) \Rightarrow p (x) = x^{2} + 7 x + 5 x + 35 \Rightarrow p (x) = x (x + 7) + 5 (x + 7) \Rightarrow p (x) = (x + 5) (x + 7) \end{matrix}$

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