(Q13) Sample #1, Math 141/146 common final, Glendale community college

TL;DR

Learn how to solve quadratic equations by factoring, using a step-by-step process to find the correct factors.

Transcript

all right this is the question that I like the most on this practice test we are going to solve this equation by factoring and here you see that we have t to the second power this is a quadratic equation and we also have learned the quadratic formula and the completing Square technique for this but let's try it with factoring first of all you need ... Read More

Key Insights

• ❎ Quadratic equations can be solved by factoring, completing the square, or using the quadratic formula.
• 🍉 Factoring involves finding two numbers that multiply to give the middle term and add up to give the last term of the equation.
• 🧑‍🏭 The T-chart method can help organize the process of finding the correct factors in a quadratic equation.
• 😫 By setting each factor equal to zero and solving separately, you can find the possible solutions of the quadratic equation.
• ❓ Quadratic equations can have two, one, or no real solutions, depending on the discriminant.
• ❓ Factoring is an efficient method for solving quadratic equations when possible.
• 🧑‍🏭 It is important to check the factors after determining them to ensure their correctness.

Questions & Answers

Q: What is the first step in solving a quadratic equation by factoring?

The first step is to ensure that one side of the equation is equal to zero, as factoring involves finding the factors of the equation to solve for T.

Q: How do you determine the correct factors in a quadratic equation?

By using a T-chart, you can consider different combinations of two numbers that multiply to give the middle term and add up to give the last term of the equation.

Q: How do you check if the factors are correct in a quadratic equation?

To check if the factors are correct, multiply the two factors and compare the result to the middle term of the equation. Additionally, multiply the remaining terms to ensure they match the last term.

Q: What are the final steps after determining the factors in a quadratic equation?

Once the factors are found, set each factor equal to zero and solve the resulting equations separately to find the possible values of T.

Summary & Key Takeaways

• To solve a quadratic equation by factoring, make sure one side is equal to zero.

• Use a T-chart to find the correct factors by thinking about what two numbers multiply to give the middle term and add up to give the last term.

• Once the factors are found, set each factor equal to zero and solve for T to find the solutions of the equation.