1. Solving Polynomial Equations
Stop! Do group activity first.

2. Solving Polynomial Equations
We already know how to solve linear and quadratic equations. Example 4𝑥−7=0 3 𝑥 2 −3𝑥−5=0

4. Solving Polynomial Equations
Cubic (3rd degree) Equations
Cubic equations can be written in the form 𝑎 𝑥 3 +𝑏 𝑥 2 +𝑐𝑥+𝑑=0.
Steps to solve:
Try to factor. If that doesn’t work…
Find one factor by trial-and-error. Then divide.
The possible solution to try are ±(𝑓𝑎𝑐𝑡𝑜𝑟𝑠 𝑜𝑓 𝑑)/(𝑓𝑎𝑐𝑡𝑜𝑟𝑠 𝑜𝑓 𝑎).
You can use Desmos to find solution quicker.
You may use synthetic division to divide the polynomials.
Test the discriminant of the remaining quadratic, and factor if necessary.

5. Solving Polynomial Equations
Example Solve 𝑥 3 − 𝑥 2 +𝑥−1=0

6. Solving Polynomial Equations
Example Solve 2𝑥 3 − 3𝑥 2 −17𝑥+30=0
Make sure you know how to do synthetic division.

7. Solving Polynomial Equations
Checkpoint Solve
Make sure you know how to do synthetic division.

9. Solving Polynomial Equations
Some higher-degree equations can be solved by pulling out the GCF or by substituting k for x2. Example
Make sure you know how to do synthetic division.