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Question:

Factorise:(i)12x² - x + 1 (ii)2x²+7x+3 (iii)6x²+5x - 6 (iv)3x²-x - 4

Solution:

(i)12x² - x + 1 = 12x² - 4x + 3x + 1 = 4x(3x - 1) + 1(3x - 1) = (4x + 1)(3x - 1)
(ii)2x²+7x+3=2x²+6x+x+3=2x(x+3)+1(x+3)=(2x+1)(x+3)
(iii)6x²+5x - 6=6x²+9x - 4x - 6=3x(2x+3) - 2(2x+3)=(3x - 2)(2x+3)
(iv)3x²-x - 4=3x² - 4x + 3x - 4=x(3x - 4) + 1(3x - 4)=(x+1)(3x - 4)