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Which equivalent four-term polynomial can be created using the [tex]$X$[/tex] method?

A. [tex] x^2 + 8x + 8x + 48 [/tex]
B. [tex] x^2 - 12x - 4x + 48 [/tex]
C. [tex] x^2 + 12x + 4x + 48 [/tex]
D. [tex] x^2 - 8x - 8x + 48 [/tex]

Sagot :

GinnyAnswer
To identify the equivalent four-term polynomial using the X method, we will follow these steps for each polynomial:

1. Simplify each polynomial by combining like terms.
2. Identify the unique simplified polynomial.

Let's examine each provided polynomial one by one:

1. For the polynomial [tex]\(x^2 + 8x + 8x + 48\)[/tex]:
- Combine the like terms: [tex]\(8x + 8x\)[/tex] becomes [tex]\(16x\)[/tex].
- Result: [tex]\(x^2 + 16x + 48\)[/tex].

2. For the polynomial [tex]\(x^2 - 12x - 4x + 48\)[/tex]:
- Combine the like terms: [tex]\(-12x - 4x\)[/tex] becomes [tex]\(-16x\)[/tex].
- Result: [tex]\(x^2 - 16x + 48\)[/tex].

3. For the polynomial [tex]\(x^2 + 12x + 4x + 48\)[/tex]:
- Combine the like terms: [tex]\(12x + 4x\)[/tex] becomes [tex]\(16x\)[/tex].
- Result: [tex]\(x^2 + 16x + 48\)[/tex].

4. For the polynomial [tex]\(x^2 - 8x - 8x + 48\)[/tex]:
- Combine the like terms: [tex]\(-8x - 8x\)[/tex] becomes [tex]\(-16x\)[/tex].
- Result: [tex]\(x^2 - 16x + 48\)[/tex].

From simplification:
- The polynomial [tex]\(x^2 + 16x + 48\)[/tex] appears in the first and third options.
- The polynomial [tex]\(x^2 - 16x + 48\)[/tex] appears in the second and fourth options.

Identifying the unique simplified polynomial, we find that [tex]\(x^2 + 16x + 48\)[/tex] is the simplified form that fits with the first given polynomial, [tex]\(x^2 + 8x + 8x + 48\)[/tex].

Hence, the equivalent four-term polynomial that can be created using the X method and is simplified to the unique form [tex]\(x^2 + 16x + 48\)[/tex] corresponds to the first option.

Thus, the answer is:
[tex]\[ \boxed{1} \][/tex]
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