Question

Find the sum of each of the following polynomials.

a)
`x^3+5x^2+2, 3x^2-4x+7`
b)
`2x + 5x^3-2x^2+7, 9+4x-5x^2-2x^3`
c)
`5x^3+2x^2+4, 2x^2+7x-5, 7-5x^2 +3x-4x^3`
d)
`2x^4-3x^2+4x^3-5, 9x^2-7x^3-2x^4, 7-x+3x^4`

Answer 1

`(a)\ Sum = x^3+8x^2-4x+9`

`(b)\ Sum =3x^3-7x^2+6x +16`

`(c)\ Sum = x^3-x^2+10x+6`

`(d)\ Sum = 3x^4 -3x^3+ 6x^2-x+2`

Explanation:

Required

Sum of the polynomials

`(a)\ x^3+5x^2+2, 3x^2-4x+7`

`Sum = x^3+5x^2+2+3x^2-4x+7`

Collect like terms

`Sum = x^3+5x^2+3x^2-4x+2+7`

`Sum = x^3+8x^2-4x+9`

`(b)\ 2x + 5x^3-2x^2+7, 9+4x-5x^2-2x^3`

`Sum =2x + 5x^3-2x^2+7+ 9+4x-5x^2-2x^3`

Collect like terms

`Sum =5x^3-2x^3-2x^2-5x^2+4x+2x +7+ 9`

`Sum =3x^3-7x^2+6x +16`

`(c)\ 5x^3+2x^2+4, 2x^2+7x-5, 7-5x^2 +3x-4x^3`

`Sum = 5x^3+2x^2+4+ 2x^2+7x-5+ 7-5x^2 +3x-4x^3`

Collect like terms

`Sum = 5x^3-4x^3+2x^2+ 2x^2-5x^2+7x+3x-5+ 7 +4`

`Sum = x^3-x^2+10x+6`

`(d)\ 2x^4-3x^2+4x^3-5, 9x^2-7x^3-2x^4, 7-x+3x^4`

`Sum = 2x^4-3x^2+4x^3-5+ 9x^2-7x^3-2x^4+ 7-x+3x^4`

Collect like terms

`Sum = 2x^4-2x^4+3x^4 +4x^3 -7x^3-3x^2+ 9x^2-x-5+ 7`

`Sum = 3x^4 -3x^3+ 6x^2-x+2`