Answer :
To determine the correct grouping of the trinomial [tex]\(-2x^2 - 9x + 35\)[/tex], we should examine which options, when regrouped, give us the original trinomial. We want to focus on ensuring that the middle terms combine to [tex]\(-9x\)[/tex].
Here's how we can solve it:
1. Understand the Original Expression:
The trinomial given is [tex]\(-2x^2 - 9x + 35\)[/tex].
2. Check each option to see which one combines back to [tex]\(-9x\)[/tex]:
- Option 1: [tex]\(-2x^2 - 16x + 7x + 35\)[/tex]
- Combine the middle terms: [tex]\(-16x + 7x = -9x\)[/tex]
- This matches the middle term of the original expression.
- Option 2: [tex]\(-2x^2 - 13x + 4x + 35\)[/tex]
- Combine the middle terms: [tex]\(-13x + 4x = -9x\)[/tex]
- This also matches the middle term of the original expression.
- Option 3: [tex]\(-2x^2 + 5x - 8x + 35\)[/tex]
- Combine the middle terms: [tex]\(5x - 8x = -3x\)[/tex]
- This does not match the original trinomial.
- Option 4: [tex]\(-2x^2 - 14x + 5x + 35\)[/tex]
- Combine the middle terms: [tex]\(-14x + 5x = -9x\)[/tex]
- This matches the middle term of the original expression.
- Option 5: [tex]\(-2x^2 + 7x - 10x + 35\)[/tex]
- Combine the middle terms: [tex]\(7x - 10x = -3x\)[/tex]
- This does not match the original trinomial.
3. Conclusion:
The correct groupings that combine to the original expression are:
- Option 1: [tex]\(-2x^2 - 16x + 7x + 35\)[/tex]
- Option 2: [tex]\(-2x^2 - 13x + 4x + 35\)[/tex]
- Option 4: [tex]\(-2x^2 - 14x + 5x + 35\)[/tex]
Therefore, any of these options would be a valid way to group the trinomial [tex]\(-2x^2 - 9x + 35\)[/tex] by combining its terms back correctly to the original expression configuration. Since the question asks for a correct grouping, any of these options are valid answers.
Here's how we can solve it:
1. Understand the Original Expression:
The trinomial given is [tex]\(-2x^2 - 9x + 35\)[/tex].
2. Check each option to see which one combines back to [tex]\(-9x\)[/tex]:
- Option 1: [tex]\(-2x^2 - 16x + 7x + 35\)[/tex]
- Combine the middle terms: [tex]\(-16x + 7x = -9x\)[/tex]
- This matches the middle term of the original expression.
- Option 2: [tex]\(-2x^2 - 13x + 4x + 35\)[/tex]
- Combine the middle terms: [tex]\(-13x + 4x = -9x\)[/tex]
- This also matches the middle term of the original expression.
- Option 3: [tex]\(-2x^2 + 5x - 8x + 35\)[/tex]
- Combine the middle terms: [tex]\(5x - 8x = -3x\)[/tex]
- This does not match the original trinomial.
- Option 4: [tex]\(-2x^2 - 14x + 5x + 35\)[/tex]
- Combine the middle terms: [tex]\(-14x + 5x = -9x\)[/tex]
- This matches the middle term of the original expression.
- Option 5: [tex]\(-2x^2 + 7x - 10x + 35\)[/tex]
- Combine the middle terms: [tex]\(7x - 10x = -3x\)[/tex]
- This does not match the original trinomial.
3. Conclusion:
The correct groupings that combine to the original expression are:
- Option 1: [tex]\(-2x^2 - 16x + 7x + 35\)[/tex]
- Option 2: [tex]\(-2x^2 - 13x + 4x + 35\)[/tex]
- Option 4: [tex]\(-2x^2 - 14x + 5x + 35\)[/tex]
Therefore, any of these options would be a valid way to group the trinomial [tex]\(-2x^2 - 9x + 35\)[/tex] by combining its terms back correctly to the original expression configuration. Since the question asks for a correct grouping, any of these options are valid answers.
