A pair of factors of - 35 that has a sum of - 2

-7,5

Step-by-step explanation:

lets take x and y as the unknown numbers

xy=-35

x+y=-2

go through all the factors of - 35

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.