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 Blanks

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

Fill in the Blanks

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 Blanks

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.