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Which of the answer choices shows the correct order in the form [tex]a x^2 + p x + q x + c[/tex] for the following trinomial: [tex]-16 x^2 - 2 x + 5[/tex]?

Select the correct answer below:

A. [tex]-16 x^2 - 2 x + 40 x + 5[/tex]

B. [tex]-16 x^2 + 8 x - 10 x + 5[/tex]

C. [tex]-16 x^2 - 7 x + 45 x + 5[/tex]

D. [tex]-16 x^2 + 10 x - 12 x + 5[/tex]

E. [tex]-16 x^2 + 3 x - 5 x + 5[/tex]

Answer :

To determine which of the answer choices correctly represents the trinomial [tex]\(-16x^2 - 2x + 5\)[/tex] in the form [tex]\(ax^2 + px + qx + c\)[/tex], we need to follow these steps:

1. Identify the Given Trinomial:
The trinomial is [tex]\(-16x^2 - 2x + 5\)[/tex].

2. Understand the Form:
The form we're looking for is [tex]\(ax^2 + px + qx + c\)[/tex]. This means the trinomial must be split into two linear terms ([tex]\(px + qx\)[/tex]) that sum up to the linear term [tex]\(-2x\)[/tex].

3. Evaluate Each Choice:

- Choice 1: [tex]\(-16x^2 - 2x + 40x + 5\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-2x + 40x = 38x\)[/tex]. This does not match [tex]\(-2x\)[/tex].

- Choice 2: [tex]\(-16x^2 + 8x - 10x + 5\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(8x - 10x = -2x\)[/tex]. This matches [tex]\(-2x\)[/tex].

- Choice 3: [tex]\(-16x^2 - 7x + 45x + 5\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-7x + 45x = 38x\)[/tex]. This does not match [tex]\(-2x\)[/tex].

- Choice 4: [tex]\(-16x^2 + 10x - 12x + 5\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(10x - 12x = -2x\)[/tex]. This matches [tex]\(-2x\)[/tex].

- Choice 5: [tex]\(-16x^2 + 3x - 5x + 5\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(3x - 5x = -2x\)[/tex]. This matches [tex]\(-2x\)[/tex].

4. Conclusion:
The choices that correctly represent the given trinomial in the form [tex]\(ax^2 + px + qx + c\)[/tex] are:
- Choice 2: [tex]\(-16x^2 + 8x - 10x + 5\)[/tex]
- Choice 4: [tex]\(-16x^2 + 10x - 12x + 5\)[/tex]
- Choice 5: [tex]\(-16x^2 + 3x - 5x + 5\)[/tex]

These choices successfully break down the linear term to sum up to [tex]\(-2x\)[/tex].

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