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
You can make some algebraic equations and solve it. The first would be: [tex]x \times y = - 21[/tex] The second would be [tex]x + y = - 4[/tex] You can then rearrange the second into [tex]x = - 4 - y[/tex] And subsitute it into the first like so: [tex]( - y - 4) \times y = - 21[/tex] After that, distribute the y into the parantheses. [tex] { - y}^{2} - 4y = - 21[/tex] Subtract the 21 on both sides and multiply by -1 on both sides: [tex] { - y}^{2} - 4y + 21 \\ {y}^{2} + 4y - 21[/tex] You then can factor it into: [tex](y + 3) \times (y - 7) = 0[/tex] 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.
