Next, let's rewrite the middle term (- 3x) as two terms ( b_1x+ b_2x). Since the expression matches the form ax^2+bx+c, we know the following.
b_1 * b_2 = ac = - 28
and
b_1 + b_2 = b = - 3
Because ac is negative we know the two terms must have opposite signs, and because b is negative we know the negative term must be larger than the positive.
c|c|c|c
1^(st)Factor
&2^(nd)Factor
&Sum
&Result
2
&- 14
&2 + (-14)
&- 12
4
& - 7
& 4 + ( - 7)
&- 3
Now, we can rewrite the equation by substituting in the values we determined above.
t^2-3t-28 = 0
⇕
t^2 + 4t - 7t -28 = 0
Finally, we can finish factoring the equation.
