To determine which of the given answer choices is a correct grouping of the trinomial [tex]\(3x^2 + 10x - 8\)[/tex], we need to verify whether combining the grouped terms yields the original trinomial. We'll examine each choice by combining like terms and checking the resulting expression.
Choice 1: [tex]\(3x^2 - 6x + 16x - 8\)[/tex]
Combine like terms:
[tex]\[3x^2 - 6x + 16x - 8 = 3x^2 + ( - 6x + 16x ) - 8 = 3x^2 + 10x - 8\][/tex]
This equals the original trinomial [tex]\(3x^2 + 10x - 8\)[/tex].
Valid
Choice 2: [tex]\(3x^2 + 0x + 10x - 8\)[/tex]
Combine like terms:
[tex]\[3x^2 + 0x + 10x - 8 = 3x^2 + ( 0x + 10x ) - 8 = 3x^2 + 10x - 8\][/tex]
This equals the original trinomial [tex]\(3x^2 + 10x - 8\)[/tex].
Valid
Choice 3: [tex]\(3x^2 - 6x + 4x - 8\)[/tex]
Combine like terms:
[tex]\[3x^2 - 6x + 4x - 8 = 3x^2 + ( - 6x + 4x ) - 8 = 3x^2 - 2x - 8\][/tex]
This does not equal the original trinomial [tex]\(3x^2 + 10x - 8\)[/tex].
Not Valid
Choice 4: [tex]\(3x^2 - 2x + 12x - 8\)[/tex]
Combine like terms:
[tex]\[3x^2 - 2x + 12x - 8 = 3x^2 + ( - 2x + 12x ) - 8 = 3x^2 + 10x - 8\][/tex]
This equals the original trinomial [tex]\(3x^2 + 10x - 8\)[/tex].
Valid
Choice 5: [tex]\(3x^2 - 10x + 8x - 8\)[/tex]
Combine like terms:
[tex]\[3x^2 - 10x + 8x - 8 = 3x^2 + ( - 10x + 8x ) - 8 = 3x^2 - 2x - 8\][/tex]
This does not equal the original trinomial [tex]\(3x^2 + 10x - 8\)[/tex].
Not Valid
From the above examination:
- Choice 1: [tex]\(3x^2 - 6x + 16x - 8\)[/tex] is valid.
- Choice 2: [tex]\(3x^2 + 0x + 10x - 8\)[/tex] is valid.
- Choice 4: [tex]\(3x^2 - 2x + 12x - 8\)[/tex] is valid.
Therefore, the correct answer is:
- [tex]\(3 x^2-6 x+16 x-8\)[/tex]
- [tex]\(3 x^2+0 x+10 x-8\)[/tex]
- [tex]\(3 x^2-2 x+12 x-8\)[/tex]
Given that multiple answer choices can be correct, we choose all those combinations that satisfy this condition.
