How to Solve Quadratic Equations by Factoring

TL;DR

To solve a quadratic equation like s² - 2s - 35 = 0, factor the left-hand side into binomials, setting each equal to zero. Using factoring by grouping, find two numbers that sum to -2 and multiply to -35, which are 5 and -7. This gives the solutions s = -5 and s = 7.

Transcript

We're asked to solve for s. And we have s squared minus 2s minus 35 is equal to 0. Now if this is the first time that you've seen this type of what's essentially a quadratic equation, you might be tempted to try to solve for s using traditional algebraic means, but the best way to solve this, especially when it's explicitly equal to 0, is to factor... Read More

Key Insights

• ❓ Factoring is an effective method for solving quadratic equations.
• 🖕 The process of factoring by grouping involves splitting the middle term to simplify the equation.
• 🟰 The product of two numbers equaling zero allows us to set both factors equal to zero and solve for the variable.

Questions & Answers

Q: What is the best way to solve quadratic equations?

The best way to solve quadratic equations, especially when it's explicitly equal to zero, is to factor the left-hand side and set each binomial equal to zero.

Q: How do you factor a quadratic equation by grouping?

To factor a quadratic equation by grouping, find two numbers whose sum is equal to the coefficient of the middle term and whose product is equal to the constant term. Split the middle term into two parts and factor out common factors from each group.

Q: What does it mean when the product of two numbers is equal to zero?

If the product of two numbers is equal to zero, it means that either one or both of the numbers must be equal to zero. This applies to the factored expressions in the quadratic equation as well.

Q: Is there a shortcut for factoring quadratic equations with a leading coefficient of 1?

Yes, when the leading coefficient is 1, you can directly factor the quadratic equation using the product of the two binomials where their sum is equal to the coefficient of the middle term and their product is equal to the constant term.

Summary & Key Takeaways

• To solve a quadratic equation, factor the left-hand side and set each binomial equal to zero.

• Use the method of factoring by grouping to split the middle term into two parts.

• Factor out common factors from each group and solve for the values of s.