what is a polynomial function? are linear and quadratic functions considered a polynomial function?

Question

when can an expression be considered NOT a polynomial?
how do you determine the degree of a term? degree of a polynomial?

Answer 1

A polynomial is an expression which combines constants, variables and exponents using multiplication, addition and subtraction. Example:



X^2 + 3*X + 7 is a polynomial



1/(X-1) + 3*X^2 is not a polynomial because of the term 1/(X-1) -- the variable cannot be in the denominator.



Consider the polynomial:



X^4 + 8X^3 - 5X^2 + 6



The degree of the polynomial is 4 it is the highest exponent to which the variable X is raised.

The degree of the term is the exponent to which the variable in the term is raised. In the example above there are four terms of degree 4, 3, 2 and 0 (the constant term has degree 0).



I hope this helps.

Answer 2

A polynomial function is any function that adheres to the structure

f(x) = a*x^n + b*x^(n-1) + ... + p*x^2 + q*x^1 + r*x^0

or f(x) = a*x^n + b*x^(n-1) + ... + p*x^2 + q*x + r



Accordingly, even a constant (e.g. f(x)=5) can be considered a polynomial function with a=b=...=p=q=0 - but you'd probably not use the terminology ;)



Hence yes, linear and quadratic functions are polynomials, too, i.e.

g(x) = q*x + r : linear

or h(x) = p*x^2 + q*x + r : quadratic



The degree is equivalent to the highest exponent, i.e. above the degree of g(x) is 1, hence "linear"; the degree of h(x) is 2, and thus "quadratic". This goes on like

degree 3: cubic

4: quartic

5: quintic

6: sextic

7: septic etc. - check out the web for more degrees and their terms (e.g. Wikipedia)

Answer 3

This Site Might Help You.



RE:

what is a polynomial function? are linear and quadratic functions considered a polynomial function?

when can an expression be considered NOT a polynomial?

how do you determine the degree of a term? degree of a polynomial?

Answer 4

What Is Polynomial Function

Answer 5

what is a polynomial function?



ANSWER

Any collection of terms added or subtracted where the exponents

of the variable are only Whole Numbers {0 , 1 , 2 , 3 , ....}

No negative or fractions for exponents, no letters under a radical





are linear and quadratic functions considered a polynomial function?



ANSWER

Yes.............y=4x - 7........y= x^2 -6x + 10





when can an expression be considered NOT a polynomial?



ANSWER

When you have negative or fractions for exponents, or letters under a radical





how do you determine the degree of a term?



ANSWER

Degree is the exponent............5X^3....Degree 3............-8x^2....Degree 2

***8x^3*y*z^5..........ADD Exponents........3 + 1 + 5............Degree 8



degree of a polynomial?



ANSWER

Is the degree of polynomial is the degree of the highest term



..................8x^3................+ 6x^2*y^5*z...................- 7y^7

Degrees.......3................2+5+1= 8..............................7......Individual terms

Degree of polynomial is...............8........................8 > 7 > 3





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Answer 6

If (2-i) is a zero, then so is (2+i) and f(x) = (x-(2-i))(x-(2+i))g(x) for some g(x) =(x^2-4x+5)g(x) So g(x) = x^3-4x^2+x-4 We can spot x=4 is a factor. So g(x) = (x-4)(x^2+1) So we have the following zeros: 2-i; 2+i; 4; i; -i and f(x) = (x-(2-i))(x-(2+i))(x-4)(x-i)(x+i)