The Fundamental Theorem of Algebra & Graphing Polynomials

School Year 2025-2026

​The Fundamental Theorem of Algebra

​Identify the number of zeros, then find all the zeros.

​Identify the number of zeros, then find all the zeros.

​Identify the number of zeros, then find all the zeros.

Multiple Choice

How many zeros will the polynomial shown have?

• 3
• 4
• 5
• 6

Fill in the Blank

Two of the zeros(roots) are -4 and -2. List all of the zeros in order from least to greatest!

-

,

-

,

.

,

Fill in the Blank

How many zeros will the polynomial shown have?

Multiple Choice

Two of the zeros(roots) are shown. What are the other zeros(roots)?

$$x^4-9x^3+23x^2-81x+126$$

• $$2,\ 7,\ 3i,\ -3i$$

• $$2,\ 7,\ 2i,\ -7i$$

• $$2,\ 7,\ 3+i,\ 3-i$$

• There are no other zeros!

Fill in the Blank

How many zeros will the polynomial shown have?

Multiple Choice

What are the roots/zeros of the equation shown:

$$x^3-x^2-11x+3$$

• $$\left[2,\ 2+i,\ 2-i\right]$$

• $$\left[2,\ 3,\ -1\right]$$

• $$\left[-2,\ 1+\sqrt[]{3},1-\sqrt[]{3}\right]$$

• $$\left[-3,\ 2+\sqrt[]{3},\ 2-\sqrt[]{3}\right]$$

Draw

Brain Break!

Draw your favorite food!

Draw

Sketch the function shown.

Draw

Sketch the function shown.