Question
Order the steps from first to last that would be used to factor: 3x^2 - 13x - 10
Steps to organize:
Find the two numbers that give a product of -30 and a sum of -13
Multiply 3 x -10
Replace the middle term with -15x and 2x.
Factor the common factor once more to get your final answer
Determine if there is a greatest common factor amongst all the terms
Factor by grouping: Take the greatest common factor out of the first two terms and the greatest common factor out of the last two terms to get 3x (x - 5) + 2 (x - 5)
Final answer: (x - 5) (3x + 2)
Steps to organize:
Find the two numbers that give a product of -30 and a sum of -13
Multiply 3 x -10
Replace the middle term with -15x and 2x.
Factor the common factor once more to get your final answer
Determine if there is a greatest common factor amongst all the terms
Factor by grouping: Take the greatest common factor out of the first two terms and the greatest common factor out of the last two terms to get 3x (x - 5) + 2 (x - 5)
Final answer: (x - 5) (3x + 2)
Answers
GPT-4o mini
Here’s the ordered list of steps to factor the expression \(3x^2 - 13x - 10\):
1. **Determine if there is a greatest common factor amongst all the terms**.
2. **Multiply 3 x -10**. (Here, -30 is obtained from multiplying \(3\) and \(-10\)).
3. **Find the two numbers that give a product of -30 and a sum of -13.** (These numbers are -15 and 2).
4. **Replace the middle term with -15x and 2x**. (This changes the expression to \(3x^2 - 15x + 2x - 10\)).
5. **Factor by grouping: Take the greatest common factor out of the first two terms and the greatest common factor out of the last two terms to get \(3x(x - 5) + 2(x - 5)\)**.
6. **Factor the common factor once more to get your final answer**.
7. **Final answer: \( (x - 5)(3x + 2) \)**.
So in order, it would be: 1, 2, 3, 4, 5, 6, 7.
1. **Determine if there is a greatest common factor amongst all the terms**.
2. **Multiply 3 x -10**. (Here, -30 is obtained from multiplying \(3\) and \(-10\)).
3. **Find the two numbers that give a product of -30 and a sum of -13.** (These numbers are -15 and 2).
4. **Replace the middle term with -15x and 2x**. (This changes the expression to \(3x^2 - 15x + 2x - 10\)).
5. **Factor by grouping: Take the greatest common factor out of the first two terms and the greatest common factor out of the last two terms to get \(3x(x - 5) + 2(x - 5)\)**.
6. **Factor the common factor once more to get your final answer**.
7. **Final answer: \( (x - 5)(3x + 2) \)**.
So in order, it would be: 1, 2, 3, 4, 5, 6, 7.