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Answer :
Let's solve the given problem step-by-step and simplify the expression:
We start with the combined expression:
[tex]\[
(4x^3 + 6x - 7) + (3x^3 - 5x^2 - 5x)
\][/tex]
1. Combine like terms:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(4x^3 + 3x^3 = 7x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: There is only one term with [tex]\(x^2\)[/tex], which is [tex]\(-5x^2\)[/tex].
- Combine the [tex]\(x\)[/tex] terms: [tex]\(6x - 5x = 1x\)[/tex] or simply [tex]\(x\)[/tex]
- Constant terms: [tex]\(-7\)[/tex] (since there is no other constant to combine with [tex]\(-7\)[/tex]).
2. Write the simplified expression:
[tex]\[
7x^3 - 5x^2 + x - 7
\][/tex]
Now, let's identify the final answer and the coefficient of [tex]\(x\)[/tex]:
- The simplified expression is [tex]\(7x^3 - 5x^2 + x - 7\)[/tex].
- The coefficient of [tex]\(x\)[/tex] in this expression is [tex]\(1\)[/tex].
Therefore, the answer to the first part of the question is option (A): [tex]\(7x^3 - 5x^2 - x - 7\)[/tex], and the coefficient of [tex]\(x\)[/tex] is indeed [tex]\(1\)[/tex].
We start with the combined expression:
[tex]\[
(4x^3 + 6x - 7) + (3x^3 - 5x^2 - 5x)
\][/tex]
1. Combine like terms:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(4x^3 + 3x^3 = 7x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: There is only one term with [tex]\(x^2\)[/tex], which is [tex]\(-5x^2\)[/tex].
- Combine the [tex]\(x\)[/tex] terms: [tex]\(6x - 5x = 1x\)[/tex] or simply [tex]\(x\)[/tex]
- Constant terms: [tex]\(-7\)[/tex] (since there is no other constant to combine with [tex]\(-7\)[/tex]).
2. Write the simplified expression:
[tex]\[
7x^3 - 5x^2 + x - 7
\][/tex]
Now, let's identify the final answer and the coefficient of [tex]\(x\)[/tex]:
- The simplified expression is [tex]\(7x^3 - 5x^2 + x - 7\)[/tex].
- The coefficient of [tex]\(x\)[/tex] in this expression is [tex]\(1\)[/tex].
Therefore, the answer to the first part of the question is option (A): [tex]\(7x^3 - 5x^2 - x - 7\)[/tex], and the coefficient of [tex]\(x\)[/tex] is indeed [tex]\(1\)[/tex].
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