Solving Polynomial Equations

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Aim: How do we solve polynomial equations using factoring?

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Presentation transcript:

Solving Polynomial Equations Stop! Do group activity first.

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

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.

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

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

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

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.