Factoring -4x^2+2x+30

In this video, we'll show you how to factor the quadratic expression -4x^2+2x+30. The first step in factoring any expression is to look for common factors that can be pulled out. In this case, we can see that -2 is a common factor, so we can rewrite the expression as

-2(2x^2 - x - 15)

Next, we use the AC method to factor the trinomial within the parentheses. The AC method involves finding two numbers that multiply to give us the product of the first and last terms (in this case, -30), and add up to give us the middle term (in this case, 2x). We can see that -6 and 5 are the two numbers that meet this requirement, so we can rewrite the expression as

-2(2x^2 - 6x + 5x - 15)

Now we can group the terms within the parentheses and factor out the common factors. We can factor out 2x from the first two terms and -5 from the last two terms, giving us

-2(2x(x - 3) + 5(x - 3))

Finally, we can see that (x - 3) is a common factor, so we can factor it out and rewrite the expression as

-2(x - 3)(2x + 5)

And there we have it! We have factored the expression -4x^2+2x+30. Remember to always check your answer by expanding the factored expression to make sure it's equivalent to the original expression.

🔍 Keywords factoring, quadratic expression, AC method, trinomial, common factors, product, middle term

1️⃣ What is the first step in factoring any expression?
- The first step is to look for common factors that can be pulled out.

2️⃣ What is the AC method used for in factoring?
- The AC method is used to factor trinomials by finding two numbers that multiply to give us the product of the first and last terms, and add up to give us the middle term.

3️⃣ What are the two numbers that multiply to -30 and add up to 2 in this expression?
- The two numbers are -6 and 5.

4️⃣ How do you factor out common factors in an expression?
- You can factor out common factors by finding the greatest common factor of the terms and dividing each term by it.

5️⃣ How do you check if your factored expression is correct?
- You can expand the factored expression to make sure it's equivalent to the original expression.

6️⃣ What is the final factored form of -4x^2+2x+30?
- The final factored form is -2(x - 3)(2x + 5).

7️⃣ What is the benefit of factoring an expression?
- Factoring an expression can help simplify it and make it easier to work with.

8️⃣ What is the difference between factoring a quadratic expression and solving a quadratic equation?
- Factoring a quadratic expression means expressing it as the product of two factors, while solving a quadratic equation means finding the values of x that make the equation true.

9️⃣ What is the FOIL method used for in algebra?
- The FOIL method is used to multiply two binomials together.

🔟 What is a trinomial?
- A trinomial is an