What is a polynomial function?

What is a polynomial function?

Lessons

Notes:

A polynomial function is a function in the form:

f(x)=anxn+an1xn1+an2xn2+f\left( x \right)\; = {a_n}{x^n} + \;{a_{n - 1}}{x^{n - 1}} + {a_{n - 2}}{x^{n - 2}} + +a2x2+a1x+a0 + {a_2}{x^2} + {a_1}x + {a_0}

\bulletcoefficients: an{a_n}, an1{a_{n - 1}}, . . . , a2{a_2}, a1{a_1}
\bulletleading coefficient: "an{a_n}", the coefficient of the highest power of x
\bulletconstant term: "a0{a_0}", the term without xx
\bulletdegree of the polynomial function: nn, the highest power of xx
    • a)
      What is a polynomial function?
    • b)
      Exercise:

      State the degree, leading coefficient and constant term for the following polynomial functions:

      1) f(x)=9x5+7x42x312x2+x10f(x) = 9x^{5}+7x^{4}-2x^{3}-12x^{2}+x-10

      2) p(x)=23x18+37x1511x58+6p(x) = -23x^{18}+37x^{15}-11x^{58}+6

  • 2.
    Recognizing a Polynomial Function

    Which of the following are not polynomial functions? Explain.

    • a)
      monomial and cubic
    • b)
      binomial and linear
    • c)
      trinomial and quartic
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What is a polynomial function?

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