Question

1. Add or Subtract. Show your work

a. (-2x^2-4x+13)+(12x^2+2x-25)

b. (7x^2+4x-26)-(-7x^2-3x+15)



2. Find the roots. List your steps correctly.

f(n)=n^2-6n-16

Answer 1

QUESTION 1a.

We want to add

`( - 2 {x}^(2) - 4x + 13) + (12 {x}^(2) + 2x - 25)`

We group similar terms to get

`- 2 {x}^(2) + 12 {x}^(2)- 4x + 2x - 25 + 13`

Simplify:

`- 10{x}^(2) - 2x -12`

QUESTION 1b.

The given function is:

`(7x^2+4x-26)-(-7x^2-3x+15)`

Expand the parenthesis to obtain,

`7x^2+4x-26 + 7x^2 + 3x - 15`

Group similar terms,

`7x^2+7 {x}^(2) + 4x + 3x-26 - 15`

Simplify:

`14{x}^(2) + 7x-41`

QUESTION 2

The given function is

`f(n)=n^2-6n-16`

The zeros of this function is given by;

`n^2-6n-16 = 0`

Split the middle term.

`n^2-8n + 2n-16 = 0`

Factor;

`n(n - 8) + 2(n - 8) = 0`

`(n - 8)(n + 2) = 0`

`n - 8 = 0 \: or \: n + 2 = 0`

`n = 8 \: or \: n = - 2`