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.
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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
Answer:
x + 3 = 14
Step-by-step explanation:
x + 3 = 14
x = 14 - 3
x = 11
Answer:
Rita's answer in incorrect because the remainder that Rita got which is 23 is greater 17 which is the divisor. 17 can still go in 23 1time to have a remainder of 6. Hence Rita's answer is wrong with 34R6 being the correct answer.
Step-by-step explanation:
Quotient is the required answer if 584 is divided by 17
584 will be the dividend and 17 is the divisor.
To calculate 584/17, 17 will go in 58 3times with 7 as remainder. This remainder 7 will combine with 4 to make 74, 17 will also go in 74 4times with remainder of 6.
The final answer by combining the number of times 17 goes in 584 which is 34 with final remainder of 6. This means that;
584/17 = 34 remainder 6 i.e 34R6
This shows that Rita's answer in incorrect because the remainder that Rita got which is 23 is greater 17 which is the divisor. 17 can still go in 23 1time to have a remainder of 6. Hence Rita's answer is wrong with 34R6 being the correct answer.
Answer:
F=1.8C+32
113°F
Step-by-step explanation:
F=1.8C+32
F=1.8(45)+32
F=81+32
F=113
