Question

Resolve each of the following quadratic trinomials into factors:

12x² - 17xy + 6y²

Answer 1

12x² – 17xy + 6y²

Here, coefficient of x² = 12, coefficient of x = -17 and constant term = 6y²

We shall now split up the coefficient of middle term i.e., -17y into two parts whose sum is -17y and product is 12 x 6y² = 72y²

Clearly,

-9y – 8y = -17y and

(-9y) (-8y) = 72y²

So, we replace middle term -17xy = - 9xy – 8xy

Thus, we have

12x² -17xy+ 6y² = 12x² - 9xy - 8xy + 6y²

= 3x (4x – 3y) – 2y (4x – 3y)

= (3x – 2y) (4x – 3y)