Answer :
To solve the problem, we need to combine the two given polynomials:
1. Identify the Polynomials:
- The first polynomial is: [tex]\( 6x^5 + 7x^3 + 9x \)[/tex]
- The second polynomial is: [tex]\( 3x^4 - 6x^3 + 7x^2 \)[/tex]
2. Combine Like Terms:
- Start by adding the coefficients of terms with the same degree (the power of [tex]\( x \)[/tex]).
3. Combine the Terms:
- [tex]\( x^5 \)[/tex] term:
- The coefficient from the first polynomial is [tex]\( 6 \)[/tex].
- There is no [tex]\( x^5 \)[/tex] term in the second polynomial.
- Combined: [tex]\( 6x^5 \)[/tex]
- [tex]\( x^4 \)[/tex] term:
- The coefficient from the first polynomial is [tex]\( 0 \)[/tex] (since it’s not present).
- The coefficient from the second polynomial is [tex]\( 3 \)[/tex].
- Combined: [tex]\( 3x^4 \)[/tex]
- [tex]\( x^3 \)[/tex] term:
- The coefficient from the first polynomial is [tex]\( 7 \)[/tex].
- The coefficient from the second polynomial is [tex]\(-6\)[/tex].
- Combine: [tex]\( 7 + (-6) = 1 \)[/tex], so [tex]\( 1x^3 \)[/tex]
- [tex]\( x^2 \)[/tex] term:
- The coefficient from the first polynomial is [tex]\( 0 \)[/tex] (since it’s not present).
- The coefficient from the second polynomial is [tex]\( 7 \)[/tex].
- Combined: [tex]\( 7x^2 \)[/tex]
- [tex]\( x \)[/tex] term:
- The coefficient from the first polynomial is [tex]\( 9 \)[/tex].
- There is no [tex]\( x \)[/tex] term in the second polynomial.
- Combined: [tex]\( 9x \)[/tex]
4. Write the Result as a Single Polynomial in Standard Form:
- Arrange the terms in descending order of the degree.
- The combined polynomial is:
[tex]\( 6x^5 + 3x^4 + 1x^3 + 7x^2 + 9x \)[/tex]
Therefore, the final single polynomial in standard form is [tex]\( 6x^5 + 3x^4 + x^3 + 7x^2 + 9x \)[/tex].
1. Identify the Polynomials:
- The first polynomial is: [tex]\( 6x^5 + 7x^3 + 9x \)[/tex]
- The second polynomial is: [tex]\( 3x^4 - 6x^3 + 7x^2 \)[/tex]
2. Combine Like Terms:
- Start by adding the coefficients of terms with the same degree (the power of [tex]\( x \)[/tex]).
3. Combine the Terms:
- [tex]\( x^5 \)[/tex] term:
- The coefficient from the first polynomial is [tex]\( 6 \)[/tex].
- There is no [tex]\( x^5 \)[/tex] term in the second polynomial.
- Combined: [tex]\( 6x^5 \)[/tex]
- [tex]\( x^4 \)[/tex] term:
- The coefficient from the first polynomial is [tex]\( 0 \)[/tex] (since it’s not present).
- The coefficient from the second polynomial is [tex]\( 3 \)[/tex].
- Combined: [tex]\( 3x^4 \)[/tex]
- [tex]\( x^3 \)[/tex] term:
- The coefficient from the first polynomial is [tex]\( 7 \)[/tex].
- The coefficient from the second polynomial is [tex]\(-6\)[/tex].
- Combine: [tex]\( 7 + (-6) = 1 \)[/tex], so [tex]\( 1x^3 \)[/tex]
- [tex]\( x^2 \)[/tex] term:
- The coefficient from the first polynomial is [tex]\( 0 \)[/tex] (since it’s not present).
- The coefficient from the second polynomial is [tex]\( 7 \)[/tex].
- Combined: [tex]\( 7x^2 \)[/tex]
- [tex]\( x \)[/tex] term:
- The coefficient from the first polynomial is [tex]\( 9 \)[/tex].
- There is no [tex]\( x \)[/tex] term in the second polynomial.
- Combined: [tex]\( 9x \)[/tex]
4. Write the Result as a Single Polynomial in Standard Form:
- Arrange the terms in descending order of the degree.
- The combined polynomial is:
[tex]\( 6x^5 + 3x^4 + 1x^3 + 7x^2 + 9x \)[/tex]
Therefore, the final single polynomial in standard form is [tex]\( 6x^5 + 3x^4 + x^3 + 7x^2 + 9x \)[/tex].
