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Simplify the expression and classify the resulting polynomial:

[tex]\((x^2 + 7x) + (2x^2 - 7x)\)[/tex]

A. Linear binomial
B. Linear monomial
C. Quadratic binomial
D. Quadratic monomial

Sagot :

GinnyAnsweridn
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
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