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4.Factorize :
i)\(12x^2 - 7x + 1\)
ii)\(2x^2 + 7x + 3\)
iii)\(6x^2 + 5x - 6\)
iv)\(3x^2 - x - 4\)
Answer :

i)\(12x^2 - 7x + 1 = 12x^2 - 4x -3x + 1\)...(by splitting middle term)
i.e. \(= 4x(3x - 1) - 1(3x - 1)\)
i.e.\(=(3x - 1)(4x - 1)\)

ii)\(2x^2 + 7x + 3 = 2x^2 + 6x + x + 3\)...(by splitting middle term)
i.e. \(= 2x(x + 3) + 1(x + 3)\)
i.e.\(=(x + 3)(2x + 1)\)

iii)\(6x^2 + 5x - 6 = 6x^2 + 9x - 4x - 6\)...(by splitting middle term)
i.e. \(= 3x(2x + 3) - 2(2x + 3)\)
i.e.\(=(2x + 3)(3x - 2)\)

iv)\(3x^2 - x - 4 = 3x^2 - 4x + 3x - 4\)...(by splitting middle term)
i.e. \(= x(3x - 4) + 1(3x - 4)\)
i.e.\(=(3x - 4)(x + 1)\)