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^4-6 x^3-2 x^2-3 x-5#?
#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#.
Unlock full access
Teacher access
Request a demo account. We will help you get started with our digital learning environment.
Student access
Is your university not a partner?
Get access to our courses via Pass Your Math independent of your university. See pricing and more.
Or visit omptest.org if jou are taking an OMPT exam.
Or visit omptest.org if jou are taking an OMPT exam.