factor:
3n^2+14n-5.
I'm stuck!
(3n -1 )(n + 5)
To factor the expression 3n^2 + 14n - 5, we need to find two binomial factors that, when multiplied, give us the original expression.
One method to factor a quadratic expression like this is by using a technique called "AC method" or "splitting the middle term." Here's how to do it:
1. Multiply the coefficient of the quadratic term (3) by the constant term (-5). In this case, 3 * -5 = -15.
2. We need to find two numbers whose product is -15 and whose sum is the coefficient of the middle term (14). In this case, the numbers are 15 and -1, because 15 * -1 = -15 and 15 + (-1) = 14.
3. Rewrite the middle term (14n) using the two numbers we found in step 2. The expression becomes 3n^2 + 15n - n - 5.
4. Group the terms: (3n^2 + 15n) + (-n - 5).
5. Factor out the GCF (Greatest Common Factor) from each group. From the first group, we can factor out 3n, and from the second group, we can factor out -1. The expression now becomes 3n(n + 5) - 1(n + 5).
6. Notice that both groups now have a common factor (n + 5). Factor out (n + 5), and you are left with (3n - 1)(n + 5).
So, the factored form of 3n^2 + 14n - 5 is (3n - 1)(n + 5).