Answer :
To subtract and simplify the given polynomials, let's break down the expression step by step:
We have two polynomials:
1. [tex]\(5x^3 - 4x + 4\)[/tex]
2. [tex]\(8x - x^2 + 3x^3 - 3\)[/tex]
The expression we need to simplify is:
[tex]\[
(5x^3 - 4x + 4) - (8x - x^2 + 3x^3 - 3)
\][/tex]
Step 1: Distribute the negative sign through the second polynomial.
[tex]\[
5x^3 - 4x + 4 - (8x) + (x^2) - (3x^3) + 3
\][/tex]
Step 2: Combine like terms.
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(5x^3 - 3x^3 = 2x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] term: [tex]\(0 + x^2 = x^2\)[/tex] (since there was no [tex]\(x^2\)[/tex] term in the first polynomial)
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-4x - 8x = -12x\)[/tex]
- Combine the constant terms: [tex]\(4 + 3 = 7\)[/tex]
Putting it all together, we get:
[tex]\[
2x^3 + x^2 - 12x + 7
\][/tex]
Thus, the simplified form of the expression is [tex]\(2x^3 + x^2 - 12x + 7\)[/tex].
Therefore, the correct answer is [tex]\((A)\)[/tex] [tex]\(2x^3 + x^2 - 12x + 7\)[/tex].
We have two polynomials:
1. [tex]\(5x^3 - 4x + 4\)[/tex]
2. [tex]\(8x - x^2 + 3x^3 - 3\)[/tex]
The expression we need to simplify is:
[tex]\[
(5x^3 - 4x + 4) - (8x - x^2 + 3x^3 - 3)
\][/tex]
Step 1: Distribute the negative sign through the second polynomial.
[tex]\[
5x^3 - 4x + 4 - (8x) + (x^2) - (3x^3) + 3
\][/tex]
Step 2: Combine like terms.
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(5x^3 - 3x^3 = 2x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] term: [tex]\(0 + x^2 = x^2\)[/tex] (since there was no [tex]\(x^2\)[/tex] term in the first polynomial)
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-4x - 8x = -12x\)[/tex]
- Combine the constant terms: [tex]\(4 + 3 = 7\)[/tex]
Putting it all together, we get:
[tex]\[
2x^3 + x^2 - 12x + 7
\][/tex]
Thus, the simplified form of the expression is [tex]\(2x^3 + x^2 - 12x + 7\)[/tex].
Therefore, the correct answer is [tex]\((A)\)[/tex] [tex]\(2x^3 + x^2 - 12x + 7\)[/tex].
