### Functions: Higher degree polynomials

### Polynomials

Polynomials

A polynomial is a function of the form

\[f(x)=a_nx^n+a_{n-1}x^{n-1}+ \ldots +a_2x^2+a_1x+a_0\]

where #a_1#, #a_2#, #\ldots#, #a_n# are numbers #a_n \ne 0# and #n# is a positive integer.

We call #n# the degree of the polynomial.

The numbers #a_1#, #a_2#, #\ldots#,#a_{n-1}#, #a_n# are called the coefficients of the polynomial and #a_n# is called the leading coefficient.

**Examples**

\[\begin{array}{rcl}f(x)&=& 2x^2+3 \\ \\ g(x)&=&4x^5+3x^2-4x+6 \\ \\ h(x)&=&-\frac{1}{2}x^6+3x^4 \\ \\ k(x)&=&5\end{array}\]

What is the degree of the polynomial #f(x)=-4 x^4+x^3+7 x^2-3 x+9#?

#4#

A polynomial is of the form #f(x)=a_nx^n+a_{n-1}x^{n-1}+ \ldots +a_2x^2+a_1x+a_0#. In which #a_1#, #a_2#, #\ldots#, #a_n# are number and #a_n \ne 0# and #n# is the degree of the polynomial.

In this case the degree is equal to #4#.

A polynomial is of the form #f(x)=a_nx^n+a_{n-1}x^{n-1}+ \ldots +a_2x^2+a_1x+a_0#. In which #a_1#, #a_2#, #\ldots#, #a_n# are number and #a_n \ne 0# and #n# is the degree of the polynomial.

In this case the degree is equal to #4#.

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