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Mathematics

Factorise :

(i) 43x2+5x−234\sqrt{3}x^2 + 5x - 2\sqrt{3}

(ii) 72x2−10x−427\sqrt{2}x^2 - 10x - 4\sqrt{2}

Factorisation

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Answer

(i) Given,

=43x2+5x−23=43x2+8x−3x−23=4x(3x+2)−3(3x+2)=(3x+2)(4x−3).\phantom{=}4\sqrt{3}x^2 + 5x - 2\sqrt{3} \\[1em] = 4\sqrt{3}x^2 + 8x - 3x - 2\sqrt{3}\\[1em] = 4x(\sqrt{3}x + 2) - \sqrt{3}(\sqrt{3}x + 2) \\[1em] = (\sqrt{3}x + 2)(4x - \sqrt{3}).

Hence, 43x2+5x−23=(3x+2)(4x−3).4\sqrt{3}x^2 + 5x - 2\sqrt{3} = (\sqrt{3}x + 2)(4x - \sqrt{3}).

(ii) Given,

=72x2−10x−42=72x2−14x+4x−42=72x(x−2)+4(x−2)=(x−2)(72x+4).\phantom{=}7\sqrt{2}x^2 - 10x - 4\sqrt{2} \\[1em] = 7\sqrt{2}x^2 - 14x + 4x - 4\sqrt{2}\\[1em] = 7\sqrt{2}x(x - \sqrt{2}) + 4(x - \sqrt{2}) \\[1em] = (x - \sqrt{2})(7\sqrt{2}x + 4).

Hence, 72x2−10x−42=(x−2)(72x+4).7\sqrt{2}x^2 - 10x - 4\sqrt{2} = (x - \sqrt{2})(7\sqrt{2}x + 4).

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