The Fundamental Theorem of Algebra

Find all zeros.

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Write a polynomial function of least degree with integral coefficients that has the given zeros.

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Find the zeros of the polynomial given one factor. Use synthetic division.

• X= 3,4,5

• x=-3,-4,-5

• x=-3,4,5

• x= 3, -4, -5

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial. 

• A

• B

• C

• D

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial. 

• A

• B

• C

• D

The Fundamental Theorem of Algebra tell us two things. Which of the options does not come from the Fundamental Theorem of Algebra?

• nth degree polynomial has at least 1 complex solution

• nth degree polynomial always has 2 x-intercepts

• nth degree polynomial has n solutions.

Determine the number of complex and real zeros for the function.

• 3 complex; 3 real

• 3 complex; 0 real

• 2 complex, 1 real

• 1 complex; 2 real

Determine the number of complex and real zeros for the function.

• 3 complex; 1 real

• 3 complex; 2 real

• 2 complex, 1 real

• 2 complex; 0 real

Determine the number of complex and real zeros for the function.

• 5 complex; 3 real

• 2 complex; 3 real

• 5 complex, 1 real

• 3 complex; 2 real

Here is a picture of a quartic polynomial. How many real solutions does this polynomial have, and how many complex solutions does this polynomial have?

• real, complex

• real, complex

• real, complex

• real, complex