to factorize the expression, GIVEN that,= 12x² - 7x + 1By splitting the middle term, we get,= 12x² - 4x - 3x +1      [(-4) × (-3) = 12 and (-4) + (-3) = -7]Take 4x as common from first two terms,= 4x(3x - 1) - 3x + 1Take -1 as common from last two terms,= 4x(3x - 1) - 1(3x - 1)Take 3x as common from both terms,= (3x - 1)(4x - 1)Which is our required answer.Given expression,= 2x² + 7x + 3By splitting the middle term, we get,= 2x² + 6x + x + 3  [6 × 1 = 2 × 3 and 6 + 1 = 7]Take 2x as common from first two terms,= 2x(x + 3) + x + 3Take 1 as common from last two terms,= 2x(x + 3) + 1(x + 3) Take (x + 3) as common from both terms,= (2x + 1)(x + 3)Which is our required answer.Given expression,= 3x² - x - 4BY splitting the middle term, = 3x² + 3x - 4x - 4  [3 - 4 = -1 and 3 × (-4) = -12]Take 3x as common from first two terms,= 3x(x + 1) - 4x - 4Take -4 as common from last two terms,= 3x(x + 1) - 4(x + 1) Take (x + 1) as common from two terms,= (x + 1)(3x - 4)Which is our required answer.The general form of a quadratic polynomial is - ax² + bx + c.We have to split B into two parts (let x and y) whose product is EQUAL to ac, i.e,→ x + y = b and XY = ac.Then, we can factorise by grouping method.