Question

The sum of the polynomials 6x3 + 8x2 – 2x + 4 and 10x3 + x2 + 11x + 9 is . Adding 3x – 2 to this sum gives a sum of .

Answer 1

The sum of polynomials
`(6x^(3) +8x^(2) +2x+4)` and
`(10x^(3) +x^(2) +11x+9)` is
`16x^(3) +9x^(2) +13x+13`.

Adding
`(3x-2)` to the sum above gives a sum of
`6x^(3) +9x^(2) +16x+11`

Explanation:

To add two polynomials, the coefficients of the terms of the same degree must be added together. The result of adding two terms of the same degree is another term of the same degree. If any term is missing from any of the grades, it can be completed with 0.

`(6x^(3) +8x^(2) +2x+4)+(10x^(3) +x^(2) +11x+9)= 16x^(3) +9x^(2) +13x+13`

If we adding
`(3x-2)` to the sum above, we get:

`(16x^(3) +9x^(2) +13x+13)+(0x^(3) +0x^(2) +3x-2)= 16x^(3) +9x^(2) +16x+11`