Solving quadratics by factoring

TL;DR

Factoring a quadratic equation allows us to find its roots or solutions by setting each factor equal to zero.

Transcript

solve for s and we have s squared minus 2s minus 35 is equal to 0. so when you have an equation like this what you want to do you're going to find that with traditional algebraic methods you're not going to be able to actually solve for s what you want to do is factor this expression on the left hand side and then use use the knowledge that if you ... Read More

Key Insights

• 🫚 Factoring is a powerful tool for solving quadratic equations as it helps find the roots or solutions of the equation.
• 🧑‍🏭 The sum and product of the factors of a quadratic equation correspond to the coefficients of the equation.
• 🧑‍🏭 If a quadratic equation cannot be factored easily, other methods like completing the square or using the quadratic formula are available.

Questions & Answers

Q: How can we solve a quadratic equation by factoring?

To solve a quadratic equation by factoring, we need to factor the equation and set each factor equal to zero. By doing so, we can find the roots or solutions of the equation.

Q: Why is factoring useful in solving quadratic equations?

Factoring allows us to break down the equation into simpler expressions and identify the roots or solutions of the equation more easily. It is a fundamental technique in algebra.

Q: What do we do if we have a quadratic equation that cannot be factored easily?

If a quadratic equation cannot be factored easily, alternative methods such as completing the square or using the quadratic formula can be employed to find the solutions.

Q: How do we verify if the solutions we found are correct?

To verify the solutions, we substitute them back into the original equation. If the equation holds true and evaluates to zero, then the solutions are correct.

Summary & Key Takeaways

• The content explains how to solve a quadratic equation by factoring.

• By factoring the equation, we can identify two numbers whose sum and product correspond to the coefficients of the quadratic equation.

• The factored equation is set to equal zero, and by applying the property that the product of two numbers is zero only if at least one of them is zero, we can find the solutions.