How do you factor the trinomial #3x^2 - 14x - 5#?
1 Answer
Multiply 3 by -5, then factor. (3x+1)(x-5)
Explanation:
The first step is to multiply 3 by -5. This yields -15.
The next step is to find the factors of -15 that add up to -14. They are -15 and 1.
The third step is to break apart the -14x into these numbers, giving you
The fourth step is to add parenthesis around the two terms next to each other.
The fifth step is to factor each term as far as possible. The first one factors down to x(3x+1) and the second one turns into -5(3x+1) If you will notice, they have the same thing being multiplied, the 3x+1. This is a good thing, and if something similar to this doesn't happen, you are doing the problem wrong.
The sixth step is to finish the problem. Take both of the terms in front of the 3x+1 and combine them, giving you x-5. Then multiply this number by one of the groups, in this case, 3x+1. This gives you your answer, (3x+1)(x-5)
