Before engaging in the discussion, view the Discussion Guidelines and the Discussion Rubric to ensure that you understand the expectations for this activity. Once you have posted your response, you are also required to respond to at least two other students’ posts. You may want to check back later to respond to your classmates.
1. Write a quadratic equation that can be solved by factoring. Solve your equation and show and explain all your work.
2. In this unit you have learned about several different ways to solve quadratic equations. How do you determine which method to use when you’re trying to solve a quadratic equation?
For your original discussion post, you only need to respond to #1 and #2.
3. View posts from your classmates and choose one to respond to. Look at the equation that your classmate created and then solve it using a method other than factoring. Show all your work. Did you get the same answer? Do you agree with your classmate’s response about determining which method to use when solving a quadratic equation? Why or why not?
4. View responses and comment on the work of another classmate. You may correct any errors that you find, show another way to solve the problem, or provide constructive feedback on the work.
1. Equations are:
3x + 2 = 5x + 8 and 7x + 2 = 7x - 4
2. The equation is:
2(32x - 2) = 2x + 36
64x - 4 = 2x + 36
plzzzz helpppp meeee
For the first equation, we want to write it in standard form: ax^2 + bx + c = 0. To do this, we can subtract 5x and 8 from both sides:
3x - 5x + 2 - 8 = 0
-2x - 6 = 0
Then, we can multiply both sides by -1 to get:
2x + 6 = 0
Now we have the equation in standard form, where a = 2, b = 0, and c = 6. To solve by factoring, we want to find two numbers that multiply to give us 6, but add to give us 0. In this case, those numbers are -3 and -2. So we can write:
2x + 6 = 0
(2x - 2)(x - 3) = 0
And we get our solutions:
2x - 2 = 0 or x - 3 = 0
2x = 2 or x = 3
x = 1
So our solution is x = 1.
For the second equation, we can simplify by dividing both sides by 2:
32x - 1 = x + 18
Now we want to get all the x terms on one side and all the constant terms on the other side. We can do this by subtracting x and 18 from both sides:
31x - 19 = 0
Now we have the equation in standard form, where a = 31, b = 0, and c = -19. To solve by factoring, we want to find two numbers that multiply to give us -589, but add to give us 0. Unfortunately, there is no such pair of numbers, which means we cannot solve this equation by factoring.
Instead, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Plugging in our values for a, b, and c, we get:
x = (-0 ± sqrt(0 + 2389)) / (2 * 31)
x = ± sqrt(77) / 31
So our solutions are:
x = sqrt(77) / 31 or x = -sqrt(77) / 31
As for determining which method to use to solve a quadratic equation, it really depends on the equation itself. If we can easily factor it, that might be the quickest method. If we can simplify the equation to make it easier to factor, that might also be a good option. If factoring doesn't work, we can use the quadratic formula or complete the square. It's all about understanding the different methods and being able to choose the best one for the situation.
tyyyyssmmmm
You're welcome! Let me know if you have any other questions.
Polynomials and Factoring Discussion
Before engaging in the discussion, view the Discussion Guidelines and the Discussion Rubric to ensure that you understand the expectations for this activity. Once you have posted your response, you are also required to respond to at least two other students’ posts. You may want to check back later to respond to your classmates.
1. Create your own question that could appear on the test for this unit. The question can be about adding, subtracting, multiplying, or factoring polynomials. Solve your own problem to make sure that the question has a solution, but do not submit your answer with your test question. Your classmates will be responsible for solving the problem that you make up.
2. What are two pieces of mathematical advice you have for a classmate who’s about to take an assessment on the content you learned in this unit? Think about what types of mistakes are common when adding, subtracting, multiplying, or factoring polynomials.
For your original discussion post, you only need to respond to #1 and #2.
3. View posts from your classmates and choose one to respond to. You will need to solve the test question that your classmate created. Be sure to show all of your work and explain your solution. Do you agree with the mathematical advice that your classmate posted? Why or why not?
4. View responses and comment on the work of another classmate. You may correct any errors that you find, show another way to solve the problem, or provide constructive feedback on the work.
1. Test question: Factor the polynomial 4x^2 + 12x - 16.
2. Two pieces of mathematical advice for a classmate would be:
- Always double-check your calculations and make sure you haven't dropped any terms or made simple arithmetic errors. These mistakes can be easy to make when working with long polynomials, so it's important to be organized and take your time.
- When factoring, try to identify any common factors between the terms first. This can make factoring much easier and faster, and can also help you avoid common mistakes like forgetting to factor out a common factor.
1. To write a quadratic equation that can be solved by factoring, we need an equation in the form of ax^2 + bx + c = 0, where a, b, and c are constants.
Let's create an example equation: x^2 + 5x + 6 = 0
To solve this equation by factoring, we will look for two numbers that multiply to give us 6, and add up to 5. Those numbers are 2 and 3, because 2 * 3 = 6, and 2 + 3 = 5.
So, we can rewrite our equation as (x + 2)(x + 3) = 0.
By applying the zero product property, we know that for the product to be zero, either (x + 2) must be zero or (x + 3) must be zero.
Setting each factor equal to zero, we get:
x + 2 = 0 --> x = -2
x + 3 = 0 --> x = -3
Therefore, the solutions to the quadratic equation x^2 + 5x + 6 = 0 are x = -2 and x = -3.
2. When determining which method to use when solving a quadratic equation, you can consider factors such as the form of the equation, the coefficients of the equation, and your proficiency with various methods.
Some common methods to solve quadratic equations include:
- Factoring: This method is suitable when the equation can be factored easily.
- Quadratic Formula: This method works for any quadratic equation, but it can be time-consuming if the coefficients are large.
- Completing the Square: This method is useful for equations that are not easily factored and don't have nice coefficient values.
- Graphing: This method can help estimate the solutions visually, but it's not very accurate.
- Using Technology: You can use calculators or online tools to solve quadratic equations quickly.
Consider the specific characteristics of the equation and choose the method that is most efficient and convenient for you.
3. (To be answered after viewing classmates' posts.)
4. (To be answered after viewing classmates' posts.)