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dlinn [17]
3 years ago
13

How do I solve polynomials

Mathematics
1 answer:
spin [16.1K]3 years ago
5 0

Answer:

Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms"

Also they can have one or more terms, but not an infinite number of terms.

These are polynomials:

3x

x − 2

−6y2 − ( 79)x

3xyz + 3xy2z − 0.1xz − 200y + 0.5

512v5 + 99w5

5

(Yes, "5" is a polynomial, one term is allowed, and it can be just a constant!)

 

These are not polynomials

3xy-2 is not, because the exponent is "-2" (exponents can only be 0,1,2,...)

2/(x+2) is not, because dividing by a variable is not allowed

1/x is not either

√x is not, because the exponent is "½" (see fractional exponents)

 

But these are allowed:

x/2 is allowed, because you can divide by a constant

also 3x/8 for the same reason

√2 is allowed, because it is a constant (= 1.4142...etc)

Monomial, Binomial, Trinomial

There are special names for polynomials with 1, 2 or 3 terms:

monomial, binomial, trinomial

Variables

Polynomials can have no variable at all

Example: 21 is a polynomial. It has just one term, which is a constant.

Or one variable

Example: x4 − 2x2 + x   has three terms, but only one variable (x)

Or two or more variables

Example: xy4 − 5x2z   has two terms, and three variables (x, y and z)

What is Special About Polynomials?

Because of the strict definition, polynomials are easy to work with.

For example we know that:

If you add polynomials you get a polynomial

If you multiply polynomials you get a polynomial

So you can do lots of additions and multiplications, and still have a polynomial as the result.

Also, polynomials of one variable are easy to graph, as they have smooth and continuous lines.

Example: x4−2x2+x

x^4-2x^2+x  

See how nice and

smooth the curve is?

You can also divide polynomials (but the result may not be a polynomial).

Degree

The degree of a polynomial with only one variable is the largest exponent of that variable.

Example:

4x3-x-3 The Degree is 3 (the largest exponent of x)

For more complicated cases, read Degree (of an Expression).

Standard Form

The Standard Form for writing a polynomial is to put the terms with the highest degree first.

Example: Put this in Standard Form: 3x2 − 7 + 4x3 + x6

The highest degree is 6, so that goes first, then 3, 2 and then the constant last:

x6 + 4x3 + 3x2 − 7

You don't have to use Standard Form, but it helps.

You might be interested in
What expessions are equivalent to 2(25)
aksik [14]

Answer:

2×25

THE ANSWER TO IT WOULD BE 50

Step-by-step explanation:

3 0
3 years ago
Suppose that cos = 12/13 what is sin what is cos 2
riadik2000 [5.3K]
First, some housekeeping:

cos = 12/13 is incomplete; "cos" must have an argument (input).

cos x = 12/13 is fine; here "cos" has the argument (input) x.

Given that cos x = 12/13, find sin x.  To do this, we'll need to find the length of the opposite side, given that the hypo length is 13 and the adj. side length is 12.

12^2 + opp^2 = 13^2, or            opp^2 = 169-144 = 25.

Then the opp side could be either 5 or -5.  Let's assume that it's +5, and that angle x is in the first quadrant.

Then sin x = opp / hyp  =  5/13   (answer)


cos 2 is an entirely different kind of problem.  Here you are told what the argument (input) to the cosine function is (it is 2, which here means 2 radians).

Using a calculator:  cos 2 = -0.416.  Note that the angle 2 rad is in QII, which is why the "adjacent side" is negative and also why the cos of 2 is negative.
8 0
3 years ago
Solve for <br> n<br> nn.<br> 7<br> n<br> −<br> 4<br> =<br> 31
makkiz [27]

Answer: 5

Step-by-step explanation:

5x7=35

35-4=31

5 0
2 years ago
Read 2 more answers
Z wants to buy five shirts worth 34 dollars each and three baseball caps worth 31
ella [17]

Answer:

$199.50

Step-by-step explanation:

10% discount of $34 = 10/100*34 = $3.40

so, a single shirt costs $34-$3.40 = $30.60

half off = 50% discount of $31 = 50/100*31 = $15.50

so, a single cap costs $31-$15.50 = $15.50

so, 5 shirts and 3 caps cost now

5*$30.60 + 3*$15.50 = $153 + $46.50 = $199.50

but careful - can this be a trick question ?

the phrasing of the problem description can also suggest that the discounts are only listed to confuse us and are already included in the mentioned prices ("worth" $34 - what does that mean ? because including the discounts they are currently "worth" their prices).

then it would just plainly be

5*$34 + 3*$31 = $170 + $93 = $263

4 0
3 years ago
6x+4=5x-6 what is the solution for it
Oksi-84 [34.3K]

Answer:

x=-10

Step-by-step explanation:

6x+4=5x-6

Subtract 5x from each side

6x-5x+4=5x-5x-6

x +4 = -6

subtract 4 from each side

x+4-4 = -6-4

x=-10

8 0
3 years ago
Read 2 more answers
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