Prefixes you will see in math (and other places) include mono-, bi-, tri-, quadri-, hexa-, poly- and others. Respectively, they mean 1, 2, 3, 4, 6, many. So, a "trinomial" is a 3-term expression. Yours has terms (n^3), (-5n^2), (-50n).
If you examine these terms, you can see that n is a factor of all of them.
There are a few things we like to do with polynomials (or trinomials, in this case). We like to perform arithmetic operations on them (addition, subtraction, multiplication, division). There is generally nothing tricky about this. The usual rules apply, and polynomial math is easier than multi-digit arithmetic in many ways.
We also like to factor polynomials. Binomials and trinomials are generally the easiest, so these are the ones you see most often. It can help to be familiar with the way binomials multiply. .. (x +a)*(x +b) .. = x*(x +b) +a*(x +b) . . . . . use the distributive property .. = x^2 +bx +ax +ab . . . . . use the distributive property twice more .. = x^2 +(a +b)x +ab . . . . . collect terms
Here, when we say "collect terms", we mean we want to combine the coefficients of "like" terms, that is, terms that have the same constellation of variables. Here, the only "like" terms are terms that have a constant multiplying the variable x. We add the terms bx and ax to get (a+b)x. (Again, the distributive property is involved. Know it backward and forward.)
When we factor out n from your trinomial, we have .. = n(n^2 -5n -50) . . . . . . using the distributive property
Comparing this to the product of binomials above, we could factor this to binomial terms if we could find "a" and "b" such that ab = -50 and (a+b) = -5. Sometimes it helps simply to list factor pairs of a number to check for possiblities. .. -50 = -50*1 = -25*2 = -10*5 The sums of these factor pairs are -49, -23, and -5. This last one matches what we are looking for as a coefficient of the linear term, so we could choose a=-10, b=5 and write your trinomial in factored form as .. = n(n -10)(n +5)
Factoring is a little trickier if the coefficient of the squared term is not 1, but it generally follows the same pattern.
_____ In summary: a trinomial is a 3-term polynomial the unusal rules for multiplying and dividing arithmetic expressions apply the process of factoring a trinomial can be helped by remembering the pattern for the product of binomials
5. Start by finding how many tiles make up the outer edge of the pool. We know that each tile is 3/4 foot, and that the entire length is 12 feet. So by doing a division, we'll find how many tiles there are: 12 ÷ 3/4 = 16. By looking at the picture, we can confirm this. By looking at the picture we also see that the pool is the same length as 14 tiles, so the fraction is 14/16 -> 7/8.
Since no innocent student will ever be caught, the probability that a student sends an email and/or text message during a lecture AND gets caught is given by the product of the probability of a student sending a message (60%) by the probability of the professor catching them (50%) :
