Answer :
To solve the given polynomial expression and classify the result, follow these steps:
1. Identify the Polynomial Expressions:
We start with two polynomials:
[tex]\[
(-9x^6 - 7x^5 - 16) + (3x^6 - 7x^5 + 14)
\][/tex]
2. Combine Like Terms:
- For the [tex]\(x^6\)[/tex] terms, combine [tex]\(-9x^6\)[/tex] and [tex]\(3x^6\)[/tex]:
[tex]\[
-9x^6 + 3x^6 = -6x^6
\][/tex]
- For the [tex]\(x^5\)[/tex] terms, combine [tex]\(-7x^5\)[/tex] and [tex]\(-7x^5\)[/tex]:
[tex]\[
-7x^5 - 7x^5 = -14x^5
\][/tex]
- For the constant terms, combine [tex]\(-16\)[/tex] and [tex]\(14\)[/tex]:
[tex]\[
-16 + 14 = -2
\][/tex]
3. Write the Simplified Polynomial in Standard Form:
Arrange the combined terms in order of decreasing degree:
[tex]\[
-6x^6 - 14x^5 - 2
\][/tex]
4. Classify the Polynomial:
- Degree: The highest power of [tex]\(x\)[/tex] in the polynomial is 6, so the degree is 6.
- Number of Terms: There are three terms in the polynomial: [tex]\(-6x^6\)[/tex], [tex]\(-14x^5\)[/tex], and [tex]\(-2\)[/tex].
In conclusion, the simplified polynomial is [tex]\(-6x^6 - 14x^5 - 2\)[/tex], classified as a sixth-degree polynomial with three terms.
1. Identify the Polynomial Expressions:
We start with two polynomials:
[tex]\[
(-9x^6 - 7x^5 - 16) + (3x^6 - 7x^5 + 14)
\][/tex]
2. Combine Like Terms:
- For the [tex]\(x^6\)[/tex] terms, combine [tex]\(-9x^6\)[/tex] and [tex]\(3x^6\)[/tex]:
[tex]\[
-9x^6 + 3x^6 = -6x^6
\][/tex]
- For the [tex]\(x^5\)[/tex] terms, combine [tex]\(-7x^5\)[/tex] and [tex]\(-7x^5\)[/tex]:
[tex]\[
-7x^5 - 7x^5 = -14x^5
\][/tex]
- For the constant terms, combine [tex]\(-16\)[/tex] and [tex]\(14\)[/tex]:
[tex]\[
-16 + 14 = -2
\][/tex]
3. Write the Simplified Polynomial in Standard Form:
Arrange the combined terms in order of decreasing degree:
[tex]\[
-6x^6 - 14x^5 - 2
\][/tex]
4. Classify the Polynomial:
- Degree: The highest power of [tex]\(x\)[/tex] in the polynomial is 6, so the degree is 6.
- Number of Terms: There are three terms in the polynomial: [tex]\(-6x^6\)[/tex], [tex]\(-14x^5\)[/tex], and [tex]\(-2\)[/tex].
In conclusion, the simplified polynomial is [tex]\(-6x^6 - 14x^5 - 2\)[/tex], classified as a sixth-degree polynomial with three terms.
