Question

Perform the indicated operation to write given polynomial in standard form: (2x^3 − 6x^2 − 7x − 2) +(x^3 +x^2 +6x − 12)

Answer 1

Answer:

$\left(2x^3-6x^2-7x-2\right)+\left(x^3+x^2+6x-12\right)=3x^3-5x^2-x-14$

Step-by-step explanation:

To add the polynomials

Remove parentheses:

$\left(2x^3-6x^2-7x-2\right)+\left(x^3+x^2+6x-12\right)=2x^3-6x^2-7x-2+x^3+x^2+6x-12$

Group like terms:

$=2x^3+x^3-6x^2+x^2-7x+6x-2-12$

Add similar elements:

$=3x^3-6x^2+x^2-7x+6x-2-12\\=3x^3-5x^2-7x+6x-2-12\\=3x^3-5x^2-x-2-12\\=3x^3-5x^2-x-14$

The Standard Form for writing down a polynomial is to put the terms with the highest degree first,its term of 2nd highest is 2nd etc..

In our case the standard form is  

$\left(2x^3-6x^2-7x-2\right)+\left(x^3+x^2+6x-12\right)=3x^3-5x^2-x-14$