How do you factorize a quadratic equation which has a coefficient of x^2 other than 1?

Factorise 6x+ x - 2 = 0

  1. Firstly, multiply the coefficient of x2 by the last number:

6 x -2 = -12

  1. List all the factors of 12 and see which pair adds/subtracts to make 1:

Factors of 12: [1,12] [2,6] [3,4]    -----------> +4 - 3 = 1

  1. Rewrite the quadratic equation, but split the x up into the above factors:

6x2 + 4x - 3x - 2 = 0

  1. Split the equation in half: 

(i) 6x2 + 4x                  (ii) -3x - 2

  1. Factorise both halves (hint: both brackets should be the same):

(i) 2x (3x + 2)              (ii) -1 (3x + 2)

  1. Place the numbers outside both brackets together into one bracket:

(2x - 1)

  1. Final answer:

6x2 + x - 2 = (2x - 1) (3x + 2)

Answered by Aleezeh A. Maths tutor

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