Question

Which of these correctly rearranges the terms in this polynomial so like terms are next to each other?
4 - 6x + 2 - 2x^2 -4x + 6x^2

Answer 1

To rearrange the polynomial \( 4 - 6x + 2 - 2x^2 - 4x + 6x^2 \) so that like terms are next to each other, we first identify the different types of terms: constant terms, linear terms (terms with \( x \)), and quadratic terms (terms with \( x^2 \)).

1. **Constant terms**: \( 4 \) and \( 2 \)
2. **Linear terms**: \( -6x \), \( -4x \)
3. **Quadratic terms**: \( -2x^2 \) and \( 6x^2 \)

Now, we can rearrange them as follows:

- Combine the constant terms: \( 4 + 2 \)
- Combine the linear terms: \( -6x - 4x \)
- Combine the quadratic terms: \( -2x^2 + 6x^2 \)

Thus, the rearrangement of the polynomial would be:

\[
(4 + 2) + (-6x - 4x) + (-2x^2 + 6x^2)
\]

This simplifies to:

\[
6 + (-10x) + (4x^2)
\]

So, the final rearranged polynomial is:

\[
6 + 4x^2 - 10x
\]

If we write it in standard form (quadratic term first), we have:

\[
4x^2 - 10x + 6
\]

This groups like terms together correctly.