Two roots of the polynomial function f(x) = x3 − 7x − 6 are −2 and 3. use the fundamental theorem of algebra and the complex conjugate theorem to determine the number and nature of the remaining root(s). explain your thinking.

The degree of the polynomial is 3.

By the fundamental theorem of algebra, the function has three roots.

Two roots are given, so there must be one root remaining.

By the complex conjugate theorem, imaginary roots come in pairs.

The final root must be real.

Step-by-step explanation:

( x³ - 7 x - 6 ) : ( x + 2 ) = x² - 2 x - 3

-x³ - 2 x²

     - 2 x² - 7 x

        2 x² +4 x

                - 3 x - 6

                  3 x + 6

                  R(x) = 0

The polynomial: x³ - 7 x - 6  =  ( x + 2) ( x² - 2 x - 3  )

x² - 2 x - 3 = x² - 3 x + x - 3 = x ( x - 3 ) + ( x - 3 ) = ( x + 1 ) ( x - 3 )

The polynomial has roots : -2, 1, 3.

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what relationship between ideas is shown in the text above?

question 1 options:

location of events

similarity of events

timing of events

examples of an idea

step-by-step explanation: