Answer:
(3x - 2)
Step-by-step explanation:
6x² - 7x + 2 can be factored using the trial and error method, the AC method, factoring by grouping, or using the quadratic formula
i will use factoring by grouping to solve
to factor by grouping: we divide the expression into 4 terms. since there are only 3 terms, we need to expand the expression. to do this, we can write 7x as a subtraction.
6x² - 3x - 4x + 2
now that we have 4 terms, we can factor by grouping by dividing the expression in half:
(6x² - 3x) (-4x + 2)
lets look at 6x² - 3x: what GCF do they have in common? both have 3x as a common factor so we will factor out 3x from the expression
3x (2x - 1)
now we take a look at -4x + 2: what GCF do they have in common? we want to have (2x - 1) as a result of the factoring job, so what number gives us that? we would have to get rid of that negative, so lets factor out -2 from the expression:
-2 (2x - 1)
the expression looking like the following:
3x (2x - 1) - 2 (2x - 1)
we can put 3x and -2 into their own factor as we have 2x - 1 as a factor already and there is no need to repeat that
(3x - 2) (2x - 1)
the missing factor is (3x - 2)
