1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Free_Kalibri [48]
3 years ago
12

We are learning polynomials in algebra one. Can anyone help explain trinomials like- n^3 - 5n^2 - 50n

Mathematics
1 answer:
murzikaleks [220]3 years ago
7 0
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
You might be interested in
Which relation is a function
Alla [95]
Every x value should have only one value of y.
So the answer is the last choice.
8 0
3 years ago
Read 2 more answers
Help ASAP Please check to see if I have the last part correct. Thanks
7nadin3 [17]
<span>In 10 repetitions, there was an instance where 3 or more out of 5 free throw missed. So the probability of her missing 3 or more out of 5 free throw is 0/10=0% or 0.0%. I</span>t appears that your answer of 0% is correct given your experiment.
3 0
3 years ago
Read 2 more answers
Y+2=2/5(x+6) write in standard form​
icang [17]

y+2=(2/5)(x+6)

5(y+2)=2(x+6)

5y+10=2x+12

-2x+5y+10-12=0

-2x+5y-2=0

2x-5y+2=0

8 0
2 years ago
E) During free time in school Zain finished 7/8 of the problems from his
TiliK225 [7]

Answer:

Ismail

Step-by-step explanation:

because he did 2/3

5 0
2 years ago
What is -5 2/3 divided by -3?
sweet [91]
The answer to this question is 1.88888888889 or rounded to 2.0
6 0
3 years ago
Other questions:
  • What is true about the completely simplified sum of the polynomials 3x squared y squared minus 2 x y to the power of 5 and negat
    12·1 answer
  • What i the product ? (2x-1)(x+4)​
    5·2 answers
  • A cafeteria sells entrees and additional items. An entree costs $4.75, and each additional item costs $1.25. A customer pays $9.
    6·2 answers
  • There are 12 sixth graders, 11 seventh
    12·1 answer
  • Please hurry <br> Select all the points that are on the graph of the line<br> 3x + 5y = 20 ?
    12·1 answer
  • Need help with 7, 8, and 9 plz :]
    15·1 answer
  • Please help will give brainliest!! thank u
    12·1 answer
  • What is the equation of the line –3x–2y=30 in slope-intercept form?
    7·2 answers
  • A triangle is located on a three-dimensional coordinate plane. Matrix A shows the location of each vertex, where the first colum
    14·2 answers
  • What is a necessary step for constructing perpendicular lines through a point off the line?
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!