Finding zeros of polynomials (example 2) | Mathematics III | High School Math | Khan Academy

TL;DR

The video explains how to find the real zeros of a polynomial by factoring and solving for x values.

Transcript

• So I have the polynomial p of x here, and p of x is being expressed as a fourth degree polynomial times three x minus eight squared, so this would actually give you some, this would give you nine x squared and a bunch of other stuff, and then you multiply that times this. It would actually give you a sixth degree polynomial all in all, but our go... Read More

Key Insights

• 😑 The polynomial equation is expressed as a product of two factors.
• 🧑‍🏭 Factoring by grouping is used to simplify the equation and find common factors.
• 0️⃣ The real zeros of the polynomial equation are the x values that make the equation equal to zero.

Questions & Answers

Q: What is the goal in finding the real zeros of a polynomial?

The goal is to determine the x values that make the polynomial equation equal to zero.

Q: How can the given polynomial equation be solved for its real zeros?

By factoring the equation and setting each factor equal to zero, the real zeros can be found.

Q: What does it mean to factor by grouping?

Factoring by grouping involves rearranging the terms of a polynomial equation to find common factors and simplify the expression.

Q: How are the x values representing the zeros of the polynomial determined?

The x values representing the zeros are found by setting each factor of the factored polynomial equation equal to zero and solving for x.

Summary & Key Takeaways

• The video teaches how to find the x values that make a polynomial equation equal to zero.

• The process involves factoring the equation and setting each factor equal to zero.

• Two real zeros are found for the given polynomial equation.