Pre-Calculus 12 Notes

By: Gen L.

Lesson 5: Solving Polynomial Equations

Solving

Solving requires more steps than factoring:

• Solve

How to Solve

Here's how to solve:

1. Set the polynomial to equal 0
2. Factor the polynomial
3. Find the roots.

Example

Solve

1. Set to 0

2. Synthetic Divide

Example, cont.

3. Factor

4. Set factors to zero.

Solving non-Factorable Factors

• Solve

1. Synthetic Divide

• , but the second factor is more challenging.

Quad Formula: The -Formula

Let's take our quadratic .

1. Get the midpoint: and the Product:
2. Here's the formula:
3. Use the formula.

Trivial Solutions

• Solve
• We could factor this, but there's an easier way.
• , among others.

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