I need help factoring this out
6a^2-5a+1
okay so now after revising
(3a-1)(2a )
the last part i don't know how to actually get -5 and 1
Factoring is not my strong suit. However, by the term "+1", you know that both of the signs in your parenthesis are going to be the same (both positive or both negative). By the term "-5a", it's a pretty good guess they'll be negative, because you can't get a negative number by multiplying two positives. So start like this:
( - )( - )
You started off right with the 3a and the 2a. For the last term (+1), you need two factors that will give you 1. The only choices are 1 and 1 or -1 and -1.
You'll find the solution to be
(3a - 1 )(2a - 1 )
To further explain how to factor the expression 6a^2 - 5a + 1, we can use a technique called the "ac method." This method involves finding two numbers that, when multiplied together, give you the product of the coefficient of the quadratic term (6 in this case) and the constant term (1 in this case), and also add up to the coefficient of the linear term (-5 in this case).
In this example, the product of 6 and 1 is 6. We need to find two numbers that multiply to 6 and add up to -5. These numbers are -2 and -3.
So now we can rewrite the middle term -5a as -2a - 3a:
6a^2 - 2a - 3a + 1
Next, group the expression into two parts:
(6a^2 - 2a) + (-3a + 1)
Now, we can factor out the common terms from each group:
2a(3a - 1) - 1(3a - 1)
Notice that we have a common factor of (3a - 1) in both terms. We can now factor it out:
(2a - 1)(3a - 1)
Therefore, the factored form of the expression 6a^2 - 5a + 1 is (2a - 1)(3a - 1).