## Solutions

### 1. #1 a-d

To find k in these questions, you must divide the numerical coefficient of the x  term by two and then square the result and substitute for k.

1a)  x + 2x + k

() = 1  Therefore, the equation becomes x + 2x + 1 and written in factored form becomes (x + 1)

1b) x - 6x + k

() = 9  Therefore, the equation becomes x - 6x + 9 and written in factored form becomes (x - 3)

1c) x - 3x + k

() =   Therefore, the equation becomes x - 3x +  and written in factored form becomes (x - )

1d) x + x + k                        (x) =  or  in lowest terms.  So,

() =   Therefore, the equation becomes xx + and written in factored form becomes (x + )