Question

Order the steps from first to last that would be used to factor: 3x² - 13x 10 (7 points) - = Determine if there is a greatest common factor amongst all the terms. = Factor the common factor once more to get your final answer. = Final answer: (x 5) (3x+2) = Multiply 3 × -10 = Find the two numbers that give a product of -30 and a sum of -13. = 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) = Replace the middle term with -15x and 2x.

Answer 1

To factor the expression $3x^2-13x-10$ step by step, we would follow the order of operations provided and clarify some points along the way. Here’s the correct sequence to achieve the desired result:

1. Determine if there is a greatest common factor amongst all the terms.
   (In this case, there isn't a GCF other than 1 for the coefficients.)

2. Multiply 3 × -10.
   (This gives us -30 which is the product of the leading coefficient and the constant term.)

3. Find the two numbers that give a product of -30 and a sum of -13.
   (The numbers are -15 and 2 because -15 × 2 = -30 and -15 + 2 = -13.)

4. Replace the middle term with -15x and 2x.
   (This gives us the expression: $3x^2-15x+2x-10$.)

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.
   (This results in $3x(x-5)+2(x-5)$.)

6. Factor the common factor once more to get your final answer.
   (Now, factor out $(x-5)$ to obtain $(x-5)(3x+2)$.)

7. Final answer: (x - 5)(3x + 2).

So the ordered steps are as follows:

1. Determine if there is a greatest common factor amongst all the terms.
2. Multiply 3 × -10.
3. Find the two numbers that give a product of -30 and a sum of -13.
4. Replace the middle term with -15x and 2x.
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: $(x-5)(3x+2)$.