To find the sum of the polynomials [tex]\(6x + 7\)[/tex] and [tex]\(8x^2 + 5x - 1\)[/tex], we need to add the corresponding terms. I'll break down the process step-by-step:
1. Identify like terms in both polynomials. Like terms are terms that have the same variable raised to the same power.
- For [tex]\(6x + 7\)[/tex], the terms are:
- [tex]\(6x\)[/tex] (linear term with [tex]\(x\)[/tex])
- [tex]\(7\)[/tex] (constant term)
- For [tex]\(8x^2 + 5x - 1\)[/tex], the terms are:
- [tex]\(8x^2\)[/tex] (quadratic term with [tex]\(x^2\)[/tex])
- [tex]\(5x\)[/tex] (linear term with [tex]\(x\)[/tex])
- [tex]\(-1\)[/tex] (constant term)
2. Arrange the polynomials in a way that aligns like terms. We write one polynomial under the other, aligning terms with the same degree:
[tex]\[
\begin{array}{r}
8x^2 + 5x - 1 \\
+ (6x + 7) \\
\end{array}
\][/tex]
3. Add the coefficients of like terms:
- For the [tex]\(x^2\)[/tex] term: There is no [tex]\(x^2\)[/tex] term in [tex]\(6x + 7\)[/tex], so the [tex]\(x^2\)[/tex] term will just be [tex]\(8x^2\)[/tex].
- For the [tex]\(x\)[/tex] term:
[tex]\[
5x + 6x = 11x
\][/tex]
- For the constant term:
[tex]\[
-1 + 7 = 6
\][/tex]
4. Write the final sum by combining all these resultant terms:
[tex]\[
8x^2 + 11x + 6
\][/tex]
Therefore, the sum of the polynomials [tex]\(6x + 7\)[/tex] and [tex]\(8x^2 + 5x - 1\)[/tex] is:
[tex]\[
8x^2 + 11x + 6
\][/tex]
