Answer :
To solve the problem of adding the polynomials [tex]\((2x^6 + 7x^5 + 4x)\)[/tex] and [tex]\((2x^6 + 6x^5 + 7x)\)[/tex], follow these steps:
1. Identify Like Terms:
- The polynomials have like terms which are the same powers of [tex]\(x\)[/tex]. Specifically, we will look for terms with [tex]\(x^6\)[/tex], [tex]\(x^5\)[/tex], and [tex]\(x\)[/tex].
2. Add the Like Terms:
- For [tex]\(x^6\)[/tex]: Add the coefficients of [tex]\(x^6\)[/tex] from both polynomials:
- [tex]\(2 + 2 = 4\)[/tex]
- For [tex]\(x^5\)[/tex]: Add the coefficients of [tex]\(x^5\)[/tex] from both polynomials:
- [tex]\(7 + 6 = 13\)[/tex]
- For [tex]\(x\)[/tex]: Add the coefficients of [tex]\(x\)[/tex] from both polynomials:
- [tex]\(4 + 7 = 11\)[/tex]
3. Write the Resultant Polynomial:
- Combine the results of the addition to express the final polynomial:
- The resulting polynomial is: [tex]\(4x^6 + 13x^5 + 11x\)[/tex]
Thus, the sum of the polynomials [tex]\((2x^6 + 7x^5 + 4x) + (2x^6 + 6x^5 + 7x)\)[/tex] is [tex]\(4x^6 + 13x^5 + 11x\)[/tex].
1. Identify Like Terms:
- The polynomials have like terms which are the same powers of [tex]\(x\)[/tex]. Specifically, we will look for terms with [tex]\(x^6\)[/tex], [tex]\(x^5\)[/tex], and [tex]\(x\)[/tex].
2. Add the Like Terms:
- For [tex]\(x^6\)[/tex]: Add the coefficients of [tex]\(x^6\)[/tex] from both polynomials:
- [tex]\(2 + 2 = 4\)[/tex]
- For [tex]\(x^5\)[/tex]: Add the coefficients of [tex]\(x^5\)[/tex] from both polynomials:
- [tex]\(7 + 6 = 13\)[/tex]
- For [tex]\(x\)[/tex]: Add the coefficients of [tex]\(x\)[/tex] from both polynomials:
- [tex]\(4 + 7 = 11\)[/tex]
3. Write the Resultant Polynomial:
- Combine the results of the addition to express the final polynomial:
- The resulting polynomial is: [tex]\(4x^6 + 13x^5 + 11x\)[/tex]
Thus, the sum of the polynomials [tex]\((2x^6 + 7x^5 + 4x) + (2x^6 + 6x^5 + 7x)\)[/tex] is [tex]\(4x^6 + 13x^5 + 11x\)[/tex].
