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X² - 5 x + 6 = x² - 3 x -2 x + 6 = x (x -3) -2 (x -3)

= (x-2) (x-3)

= (x-2) (x-3)

The first term is, 2x2 its coefficient is 2 .

The middle term is, -5x its coefficient is -5 .

The last term, "the constant", is -3

Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -6

Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -5 .

-6 + 1 = -5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 1

2x2 - 6x + 1x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

2x • (x-3)

Add up the last 2 terms, pulling out common factors :

1 • (x-3)

Now add up the four terms of step 3 :

(2x+1) • (x-3)

Which is the desired factorization