Order the steps from first to last that would be used to factor:

Question

3213-10

(7 points)

Replace the middle term with-15z and 22.

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 3z (z-5)+2(2-5)

Multiply 3x-10

Factor the common factor once more to get your final answer.

Find the two numbers that give a product of -30 and a sum of -13.

Determine if there is a greatest common factor amongst all the terms.

Final answer: (x-5) (3z+2)

Answer 1

To factor the expression \( 3213 - 10 \) using the given steps, let's order them logically from first to last:

1. Determine if there is a greatest common factor amongst all the terms.
2. Replace the middle term with -15z and 22.
3. Find the two numbers that give a product of -30 and a sum of -13.
4. 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 3z (z-5) + 2(2-5).
5. Multiply 3x - 10.
6. Factor the common factor once more to get your final answer.
7. Final answer: (x-5)(3z+2).

This order follows a logical progression for factoring an expression. Note that the initial expression \( 3213 - 10 \) seems more like a number rather than an algebraic expression, which could cause confusion when referencing middle terms and factors. If you have a specific algebraic expression in mind, please provide that for further assistance!