Factor trinomial by grouping : 10x^2-9x+2

(2x - 1) (5x - 2)

Step-by-step explanation:

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x - term, that is

product = 10 * 2 = 20 and sum = - 9

The factors are - 5 and - 4

Split the middle term using these factors

10x² - 5x - 4x + 2 (factor the first/second and third/fourth terms by grouping)

= 5x (2x - 1) - 2 (2x - 1) ← factor out (2x - 1)

= (2x - 1) (5x - 2)