Answer :

To add the polynomials [tex]\((8x^4 - 9x^3 - 6x) + (4x^4 + 10x^3 - 4)\)[/tex], follow these steps:

1. Identify Like Terms:
- Terms with [tex]\(x^4\)[/tex]: [tex]\(8x^4\)[/tex] and [tex]\(4x^4\)[/tex]
- Terms with [tex]\(x^3\)[/tex]: [tex]\(-9x^3\)[/tex] and [tex]\(10x^3\)[/tex]
- Terms with [tex]\(x\)[/tex]: [tex]\(-6x\)[/tex] (from the first polynomial, no [tex]\(x\)[/tex]-term in the second polynomial)
- Constant terms: There is no constant term in the first polynomial, and [tex]\(-4\)[/tex] in the second polynomial.

2. Add the Coefficients of Like Terms:
- For [tex]\(x^4\)[/tex]: [tex]\(8 + 4 = 12\)[/tex], so the term is [tex]\(12x^4\)[/tex].
- For [tex]\(x^3\)[/tex]: [tex]\(-9 + 10 = 1\)[/tex], so the term is [tex]\(1x^3\)[/tex].
- For [tex]\(x^2\)[/tex]: There are no [tex]\(x^2\)[/tex] terms in either polynomial, so this remains [tex]\(0x^2\)[/tex].
- For [tex]\(x\)[/tex]: [tex]\(-6\)[/tex] (since there is no [tex]\(x\)[/tex] term in the second polynomial).
- For the constant: [tex]\(0 - 4 = -4\)[/tex].

3. Write the Resulting Polynomial:
- Combine all these results to form the new polynomial: [tex]\(12x^4 + 1x^3 + 0x^2 - 6x - 4\)[/tex].

So, the sum of the polynomials is [tex]\(12x^4 + 1x^3 - 6x - 4\)[/tex].

Thanks for taking the time to read Add the two polynomials tex left 8x 4 9x 3 6x right left 4x 4 10x 3 4 right tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada