## 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 x+ x + and written in factored form becomes (x + )