What does the degree of a polynomial expression tell you about its related polynomial function? Explain your thinking. Give an example of a polynomial expression of degree three. Provide information regarding the graph and zeros of the related polynomial function.

The polynomial degree relates to the number of "zeros" or points of intersection of the polynomial function (curve in the (x,y) plane) with the x axis (that is, points where y=0). These zeros can sometimes be coinciding but that phenomenon aside, you will see N such intercepts with the x axis for a polynomial expression of N-th degree.

Example of a polynomial of 3rd degree is: x^3 + 2 x^2 - x - 2

You can factor it to (x-1)(x+1)(x+2) to see that the zeros are +1, -1, and -2. The plot is attached as an image - note the intercepts. Lmk if you have questions.

shristiparmar1221 shristiparmar1221 · Answer 2 · 2021-12-01T10:30:02+01:00

A degree in a polynomial function is the greatest exponent of that equation, which determines the most number of solutions that a function could have and the most number of times a function will cross the x-axis when graphed or we can also say that degree of polynomial determines the number of zeroes of that polynomial function.

Let us take an example of polynomial expression of degree three,

For e.g. [tex]x^{3}+2x^{2} -x-2=0[/tex] ...(1)

By hit and trial method we have to solve it .

Firstly, we put [tex]x = +1[/tex] in above equation ,

We get , [tex]1+2-1-2=0[/tex]

Thus, x = +1 is first zero of the equation.

Now ,we put [tex]x = -1[/tex] in equation...(1) ,

We get,

[tex]-1+2-(-1)-2=0[/tex]

i.e. x = -1 is also second zero of the equation.

Then, we put [tex]x = -2[/tex] in equation...(1) ,

We get ,

[tex]-8+8-(-2)-2=0[/tex]

Thus, the third zero of the equation is x = -2.

Therefore there are three zeroes of the polynomial function are x = -1, +1 and -2.

For more information, please prefer this link :

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