Order the steps from first to last that would be used to factor: 3x^2 - 13x - 10

Question

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)

Answer 1

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.