Answer :
To simplify the expression [tex]\((4x^3 + 6x - 7) + (3x^3 - 5x^2 - 5x)\)[/tex], follow these steps:
1. Combine Like Terms:
- For [tex]\(x^3\)[/tex] terms:
- Add the coefficients of the [tex]\(x^3\)[/tex] terms from both polynomials. We have:
[tex]\[
4x^3 + 3x^3 = 7x^3
\][/tex]
- For [tex]\(x^2\)[/tex] terms:
- Combine the coefficients of the [tex]\(x^2\)[/tex] terms. Note that there is no [tex]\(x^2\)[/tex] term in the first polynomial, so we consider it as [tex]\(0x^2\)[/tex]:
[tex]\[
0x^2 - 5x^2 = -5x^2
\][/tex]
- For [tex]\(x\)[/tex] terms:
- Combine the coefficients of the [tex]\(x\)[/tex] terms:
[tex]\[
6x - 5x = 1x
\][/tex]
- For constant terms:
- Add the constant numbers:
[tex]\[
-7 + 0 = -7
\][/tex]
2. Write the Simplified Expression:
Combine all the results from above:
[tex]\[
7x^3 - 5x^2 + x - 7
\][/tex]
Thus, the simplest form of the given expression is [tex]\(7x^3 - 5x^2 + x - 7\)[/tex].
So, the correct answer is B. [tex]\(7x^3 - 5x^2 + x - 7\)[/tex].
1. Combine Like Terms:
- For [tex]\(x^3\)[/tex] terms:
- Add the coefficients of the [tex]\(x^3\)[/tex] terms from both polynomials. We have:
[tex]\[
4x^3 + 3x^3 = 7x^3
\][/tex]
- For [tex]\(x^2\)[/tex] terms:
- Combine the coefficients of the [tex]\(x^2\)[/tex] terms. Note that there is no [tex]\(x^2\)[/tex] term in the first polynomial, so we consider it as [tex]\(0x^2\)[/tex]:
[tex]\[
0x^2 - 5x^2 = -5x^2
\][/tex]
- For [tex]\(x\)[/tex] terms:
- Combine the coefficients of the [tex]\(x\)[/tex] terms:
[tex]\[
6x - 5x = 1x
\][/tex]
- For constant terms:
- Add the constant numbers:
[tex]\[
-7 + 0 = -7
\][/tex]
2. Write the Simplified Expression:
Combine all the results from above:
[tex]\[
7x^3 - 5x^2 + x - 7
\][/tex]
Thus, the simplest form of the given expression is [tex]\(7x^3 - 5x^2 + x - 7\)[/tex].
So, the correct answer is B. [tex]\(7x^3 - 5x^2 + x - 7\)[/tex].
