Question: "If p and q are constants and x2+px+12 is equivalent to (x+3)(x+q), what is the value of p?"
I was told that the answer was 7 but I am not sure how to reach this value myself.
2. Homework Equations
I am not quite sure if this is applicable.
The Attempt at a Solution
1) To start I read the problem and saw that it said the two expressions were equivalent. So I set them equal to each other: x2+px+12=(x+3)(x+q)
2A) At this point I am confused about what to do next, so I try multiplying out the two factors: x2+px+12=x2+xq+3x+3q. With this I do not know what to do next, I believe I may have made things harder to solve and that this step was not useful. I then decide to start over and attempt to factor the trinomial from the question.
2B) x2+px+12: I have attempted to factor out the trinomial in the way I remember factoring in the past... This proved to be even more challenging. I started by multiplying the coefficient of x2 1 by the constant 12, I got 12. Then I try to find the factors of 12, I find 1 and 12, 2 and 6, and 3 and 4. However obviously none of these factors can be added to equal the middle term.
I am not sure if my mistake was setting the two expressions equal to each other, multiplying the two factors, attempting to factor the trinomial, or something else entirely.
This is my first day posting homework on the Physics Forum and I am not sure if I am doing it right. I realize that i did not even provide an attempted answer so please let me know if this is unacceptable, also if I did anything else wrong in this post please inform me. Thanks for the help!