Question

Factorise:x^2-4x-12032

Answer 1

Answer:

$\large{\bold{x^2-4x-12032=(x-2(1-\sqrt{3009}))(x-2(1+\sqrt{3009}))}}$

Step-by-step explanation:

$x^2-4x-12032\\\\=x^2-4x+4-(12036)\\\\=(x-2)^2-(\sqrt{12036})^2\\\\=(x-2)^2-(\sqrt{4\times3009})^2\\\\=(x-2)^2-(2\sqrt{3009})^2\\\\=(x-2+2\sqrt{3009})(x-2-2\sqrt{3009})\\\\=(x-2(1-\sqrt{3009}))(x-2(1+\sqrt{3009}))\\\\\\FORMULAE\\\\(a-b)^2=a^2-2ab+b^2\\\\(a^2-b^2)=(a+b)(a-b)$

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