Question

Which polynomial represents the sum: `(5x^4-3x^2-2x)+(2x^4+2x^3+2x^2+x+1)`?

Answer 1

See a solution process below:

Explanation:

First, remove all of the terms from parenthesis. Be careful to handle the signs of each individual term correctly:

`5x^4 - 3x^2 - 2x + 2x^4 + 2x^3 + 2x^2 + x + 1`

Next, group like terms:

`5x^4 + 2x^4 + 2x^3 - 3x^2 + 2x^2 - 2x + x + 1`

Now, combine like terms:

`5x^4 + 2x^4 + 2x^3 - 3x^2 + 2x^2 - 2x + 1x + 1`

`(5 + 2)x^4 + 2x^3 + (-3 + 2)x^2 + (-2 + 1)x + 1`

`7x^4 + 2x^3 + (-1)x^2 + (-1)x + 1`

`7x^4 + 2x^3 - 1x^2 - 1x + 1`

`7x^4 + 2x^3 - x^2 - x + 1`