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)  xblank squared + 2x + k

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

1b) xblank squared - 6x + k

(fraction numerator negative 6 over denominator 2 end fraction)blank squared = 9  Therefore, the equation becomes xblank squared - 6x + 9 and written in factored form becomes (x - 3)blank squared

1c) xblank squared - 3x + k

(fraction numerator negative 3 over denominator 2 end fraction)blank squared = 9 over 4  Therefore, the equation becomes xblank squared - 3x + 9 over 4 and written in factored form becomes (x - 3 over 2)blank squared

1d) xblank squared + 4 over 3x + k                        (4 over 3x1 half) = 4 over 6 or 2 over 3 in lowest terms.  So,

(2 over 3)blank squared = 4 over 9  Therefore, the equation becomes xblank squared4 over 3x +4 over 9 and written in factored form becomes (x + 2 over 3)blank squared