Answer :
To simplify the expression [tex]\((4x^3 - 3x - 7) + (3x^3 + 5x + 3)\)[/tex], we'll combine like terms from each polynomial. Here’s how you can do this step-by-step:
1. Identify the terms:
- In the first polynomial, [tex]\((4x^3 - 3x - 7)\)[/tex], we have:
- [tex]\(4x^3\)[/tex] (cubic term)
- [tex]\(-3x\)[/tex] (linear term)
- [tex]\(-7\)[/tex] (constant term)
- In the second polynomial, [tex]\((3x^3 + 5x + 3)\)[/tex], we have:
- [tex]\(3x^3\)[/tex] (cubic term)
- [tex]\(5x\)[/tex] (linear term)
- [tex]\(3\)[/tex] (constant term)
2. Combine the like terms:
- Cubic terms: Add the [tex]\(x^3\)[/tex] terms:
[tex]\[
4x^3 + 3x^3 = 7x^3
\][/tex]
- Linear terms: Add the [tex]\(x\)[/tex] terms:
[tex]\[
-3x + 5x = 2x
\][/tex]
- Constant terms: Add the constant numbers:
[tex]\[
-7 + 3 = -4
\][/tex]
3. Write the simplified expression:
[tex]\[
7x^3 + 2x - 4
\][/tex]
Therefore, the correct simplification of [tex]\((4x^3 - 3x - 7) + (3x^3 + 5x + 3)\)[/tex] is [tex]\(7x^3 + 2x - 4\)[/tex]. This corresponds to the third option given: [tex]\(7x^3 + 2x - 4\)[/tex].
1. Identify the terms:
- In the first polynomial, [tex]\((4x^3 - 3x - 7)\)[/tex], we have:
- [tex]\(4x^3\)[/tex] (cubic term)
- [tex]\(-3x\)[/tex] (linear term)
- [tex]\(-7\)[/tex] (constant term)
- In the second polynomial, [tex]\((3x^3 + 5x + 3)\)[/tex], we have:
- [tex]\(3x^3\)[/tex] (cubic term)
- [tex]\(5x\)[/tex] (linear term)
- [tex]\(3\)[/tex] (constant term)
2. Combine the like terms:
- Cubic terms: Add the [tex]\(x^3\)[/tex] terms:
[tex]\[
4x^3 + 3x^3 = 7x^3
\][/tex]
- Linear terms: Add the [tex]\(x\)[/tex] terms:
[tex]\[
-3x + 5x = 2x
\][/tex]
- Constant terms: Add the constant numbers:
[tex]\[
-7 + 3 = -4
\][/tex]
3. Write the simplified expression:
[tex]\[
7x^3 + 2x - 4
\][/tex]
Therefore, the correct simplification of [tex]\((4x^3 - 3x - 7) + (3x^3 + 5x + 3)\)[/tex] is [tex]\(7x^3 + 2x - 4\)[/tex]. This corresponds to the third option given: [tex]\(7x^3 + 2x - 4\)[/tex].
