Answer:
The pair of factors in question are x = 5 and y = -7
Step-by-step explanation:
Let the factors be represented by x and y. Then x*y = -35 and x + y = -2.
Solving the first equation for y yields x = -35/y.
Substituting -35/y for x in the second equation yields
-35/y + y = -2.
Multiplying all three terms by y yields -35 + y^2 = -2y, or
y^2 + 2y - 35 = 0.
Let's solve for y. Note that this quadratic factors easily into (y + 7)(y - 5) = 0.
Then either y = -7 or y = 5. Going back to x = -35/y and letting y = -7, we find that x = -35/(-7) = 5.
The pair of factors in question are x = 5 and y = -7, or y = -5 and x = 7.
