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)=5 x^2-7 x+5#?
#2#
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 #2#.
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 #2#.
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