Answer :
To solve the problem of grouping the trinomial [tex]\(-2x^2 - 9x + 35\)[/tex], we need to find which among the given options correctly represents a way to split the middle term, [tex]\(-9x\)[/tex], into two terms that add up to it.
Here's a step-by-step guide on how we can approach it:
1. Understand the Problem: We are given a trinomial [tex]\(-2x^2 - 9x + 35\)[/tex] and several potential ways to split the middle term. The goal is to find a correct grouping where the split terms still combine to give the original trinomial.
2. Check Each Option: We will examine each of the provided groupings to see if their middle terms combine to [tex]\(-9x\)[/tex].
- Option A: [tex]\(-2x^2 - 16x + 7x + 35\)[/tex]
- The middle terms are [tex]\(-16x\)[/tex] and [tex]\(+7x\)[/tex].
- Adding these gives: [tex]\(-16x + 7x = -9x\)[/tex], which matches the original trinomial.
- Option B: [tex]\(-2x^2 - 13x + 4x + 35\)[/tex]
- The middle terms are [tex]\(-13x\)[/tex] and [tex]\(+4x\)[/tex].
- Adding these gives: [tex]\(-13x + 4x = -9x\)[/tex].
- Option C: [tex]\(-2x^2 + 5x - 8x + 35\)[/tex]
- The middle terms are [tex]\(+5x\)[/tex] and [tex]\(-8x\)[/tex].
- Adding these gives: [tex]\(5x - 8x = -3x\)[/tex].
- Option D: [tex]\(-2x^2 - 14x + 5x + 35\)[/tex]
- The middle terms are [tex]\(-14x\)[/tex] and [tex]\(+5x\)[/tex].
- Adding these gives: [tex]\(-14x + 5x = -9x\)[/tex].
- Option E: [tex]\(-2x^2 + 7x - 10x + 35\)[/tex]
- The middle terms are [tex]\(+7x\)[/tex] and [tex]\(-10x\)[/tex].
- Adding these gives: [tex]\(7x - 10x = -3x\)[/tex].
3. Identify the Correct Answer:
- Both Option A and Option B correctly split the middle term into parts that add up to [tex]\(-9x\)[/tex]. However, the process dictates checking that the entire expression matches up.
- Given the context of the problem, the correct answer we are looking for matches Option A: [tex]\(-2x^2 - 16x + 7x + 35\)[/tex].
Hence, the correct grouping of the trinomial [tex]\(-2x^2 - 9x + 35\)[/tex] is [tex]\(-2x^2 - 16x + 7x + 35\)[/tex].
Here's a step-by-step guide on how we can approach it:
1. Understand the Problem: We are given a trinomial [tex]\(-2x^2 - 9x + 35\)[/tex] and several potential ways to split the middle term. The goal is to find a correct grouping where the split terms still combine to give the original trinomial.
2. Check Each Option: We will examine each of the provided groupings to see if their middle terms combine to [tex]\(-9x\)[/tex].
- Option A: [tex]\(-2x^2 - 16x + 7x + 35\)[/tex]
- The middle terms are [tex]\(-16x\)[/tex] and [tex]\(+7x\)[/tex].
- Adding these gives: [tex]\(-16x + 7x = -9x\)[/tex], which matches the original trinomial.
- Option B: [tex]\(-2x^2 - 13x + 4x + 35\)[/tex]
- The middle terms are [tex]\(-13x\)[/tex] and [tex]\(+4x\)[/tex].
- Adding these gives: [tex]\(-13x + 4x = -9x\)[/tex].
- Option C: [tex]\(-2x^2 + 5x - 8x + 35\)[/tex]
- The middle terms are [tex]\(+5x\)[/tex] and [tex]\(-8x\)[/tex].
- Adding these gives: [tex]\(5x - 8x = -3x\)[/tex].
- Option D: [tex]\(-2x^2 - 14x + 5x + 35\)[/tex]
- The middle terms are [tex]\(-14x\)[/tex] and [tex]\(+5x\)[/tex].
- Adding these gives: [tex]\(-14x + 5x = -9x\)[/tex].
- Option E: [tex]\(-2x^2 + 7x - 10x + 35\)[/tex]
- The middle terms are [tex]\(+7x\)[/tex] and [tex]\(-10x\)[/tex].
- Adding these gives: [tex]\(7x - 10x = -3x\)[/tex].
3. Identify the Correct Answer:
- Both Option A and Option B correctly split the middle term into parts that add up to [tex]\(-9x\)[/tex]. However, the process dictates checking that the entire expression matches up.
- Given the context of the problem, the correct answer we are looking for matches Option A: [tex]\(-2x^2 - 16x + 7x + 35\)[/tex].
Hence, the correct grouping of the trinomial [tex]\(-2x^2 - 9x + 35\)[/tex] is [tex]\(-2x^2 - 16x + 7x + 35\)[/tex].
