To solve the problem of adding the polynomials [tex]\( (5x^2 - 2x) \)[/tex] and [tex]\( (6x - 4) \)[/tex], let's follow these steps:
1. Write down the given polynomials:
[tex]\[
(5x^2 - 2x) + (6x - 4)
\][/tex]
2. Combine like terms:
- Identify the terms with [tex]\( x^2 \)[/tex], [tex]\( x \)[/tex], and the constant terms separately.
- There is only one term with [tex]\( x^2 \)[/tex], which is [tex]\( 5x^2 \)[/tex].
- For the [tex]\( x \)[/tex] terms: [tex]\(-2x\)[/tex] and [tex]\(+6x\)[/tex]
- For the constant term: [tex]\(-4\)[/tex]
3. Add the coefficients of like terms:
- The [tex]\( x^2 \)[/tex] term remains: [tex]\( 5x^2 \)[/tex].
- Combine the [tex]\( x \)[/tex] terms: [tex]\(-2x + 6x = 4x\)[/tex].
- The constant term is: [tex]\(-4\)[/tex].
4. Write the final polynomial expression:
Combining all the terms together, we get:
[tex]\[
5x^2 + 4x - 4
\][/tex]
Therefore, the combined polynomial expression is:
[tex]\[
5x^2 + 4x - 4
\][/tex]
So the correct answer is:
[tex]\[
\boxed{D. \ 5x^2 + 4x - 4}
\][/tex]
