Question

Add the polynomials.
(7x^2 - 6x + 6) + (7x^3 - 7x)

Answer 1

To add the polynomials \( (7x^2 - 6x + 6) \) and \( (7x^3 - 7x) \), we will combine like terms.

First, let's write both polynomials:

1. \( 7x^3 - 7x \)
2. \( 7x^2 - 6x + 6 \)

Now, we can align the terms by their degree:

\[
7x^3 + 7x^2 + (-6x - 7x) + 6
\]

Now combine the coefficients of the like terms:

- The \( x^3 \) term: \( 7x^3 \)
- The \( x^2 \) term: \( 7x^2 \)
- The \( x \) terms: \( -6x - 7x = -13x \)
- The constant term: \( 6 \)

Putting it all together, we have:

\[
7x^3 + 7x^2 - 13x + 6
\]

So, the sum of the polynomials is:

\[
\boxed{7x^3 + 7x^2 - 13x + 6}
\]