Question

Order the steps from first to last that would be used to factor: 3x^2 - 13x - 10
A) Determine if there is a greatest common factor amongst all the terms.
B) Final answer: (x - 5) (3x + 2)
C) Factor the common factor once more to get your final answer.
D) Find the two numbers that give a product of -30 and a sum of -13
E) 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)
F) Multiply 3 x -10
G) Replace the middle term with -152x

Answer 1

To order the steps for factoring the expression \(3x^2 - 13x - 10\), we can follow these logical steps:

1. **A)** Determine if there is a greatest common factor amongst all the terms.
2. **D)** Find the two numbers that give a product of -30 and a sum of -13.
3. **G)** Replace the middle term with -15x + 2x (the two numbers found in step D).
4. **E)** 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 \(3x (x - 5) + 2(x - 5)\).
5. **C)** Factor the common factor once more to get your final answer.
6. **B)** Final answer: \((x - 5) (3x + 2)\).

So, the correct order is: A, D, G, E, C, B.

**F)** Multiply 3 x -10 is not a necessary step in the factorization of this polynomial.