To simplify the given polynomial expression [tex]\((x^2 + 7x) + (2x^2 - 7x)\)[/tex], we should first combine like terms.
1. Identify and combine the [tex]\(x^2\)[/tex] terms:
- [tex]\(x^2\)[/tex] from the first polynomial
- [tex]\(2x^2\)[/tex] from the second polynomial
Adding these terms together, we get:
[tex]\[
x^2 + 2x^2 = 3x^2
\][/tex]
2. Next, identify and combine the [tex]\(x\)[/tex] terms:
- [tex]\(7x\)[/tex] from the first polynomial
- [tex]\(-7x\)[/tex] from the second polynomial
Adding these terms together, we get:
[tex]\[
7x - 7x = 0
\][/tex]
3. Putting it all together, the combined expression simplifies to:
[tex]\[
3x^2 + 0 = 3x^2
\][/tex]
The simplified expression is [tex]\(3x^2\)[/tex]. Now, we need to determine the classification of this polynomial.
- The degree of the polynomial is the highest power of the variable. In this case, the highest power of [tex]\(x\)[/tex] is 2, so it is a quadratic polynomial.
- The number of terms in the simplified expression is one (the term [tex]\(3x^2\)[/tex]), so it is a monomial.
Therefore, the resulting polynomial is a quadratic monomial.
The correct answer is:
D. quadratic monomial
