I need help factoring this out
6a^2-5a+1
so far what i have is this:
(3a-1)(3a )
If you expand your answer you will not get the original expression, so you are wrong.
hint: 3a x ?a = 6a^2
To factor the expression 6a^2 - 5a + 1 correctly, we need to find two binomial factors that, when multiplied together, give us the original expression.
One way to approach factoring is to use the quadratic formula. However, in this case, the expression can be factored using the "ac method."
The "ac method" involves finding two numbers that multiply to give the product of the coefficient of the quadratic term (a) and the constant term (c), and add up to the coefficient of the linear term (b).
In this case, a = 6, b = -5, and c = 1.
We need to find two numbers that multiply to give 6 * 1 = 6 and add up to -5.
The numbers that satisfy these conditions are -2 and -3.
Now, we can rewrite the middle term (-5a) as the sum of -2a and -3a:
6a^2 - 2a - 3a + 1
Now, we group the terms into two pairs and factor each pair:
(6a^2 - 2a) - (3a - 1)
We can factor out a common factor from each pair:
2a(3a - 1) - 1(3a - 1)
Notice that we now have a common binomial factor, (3a - 1).
So we can rewrite the expression as:
(2a - 1)(3a - 1)
Now, if you expand this expression, you will obtain the original expression:
(2a - 1)(3a - 1) = 6a^2 - 2a - 3a + 1
Therefore, the correct factorization is (2a - 1)(3a - 1).