Question
Order the steps from first to last that would be used to factor:
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)
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)
Answers
GPT-4o mini
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!
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!