Question

for the following two numbers, find two factors of the first number such that their product is the first number and their sum is the second number ? -21,-4

Answer 1

You can make some algebraic equations and solve it.
The first would be:
$x \times y = - 21$
The second would be
$x + y = - 4$
You can then rearrange the second into
$x = - 4 - y$
And subsitute it into the first like so:
$( - y - 4) \times y = - 21$
After that, distribute the y into the parantheses.
${ - y}^{2} - 4y = - 21$
Subtract the 21 on both sides and multiply by -1 on both sides:
${ - y}^{2} - 4y + 21 \\ {y}^{2} + 4y - 21$
You then can factor it into:
$(y + 3) \times (y - 7) = 0$
With Zero Product Property, we can determine y to be either -3 and 7. Since the variables are interchangable, you can say the same about x, just that whatever x is, y must be the other value.


Thus, the answer is 7 and -3.