To find two factors that multiply to -40 and add to -8, we can use a trial and error method or the factoring formula.
Using the factoring formula, which is:
(x + a) (x + b) = x^2 + (a+b)x + ab
where a and b are the factors we're trying to find, and x^2 + (a+b)x + ab is the original quadratic expression.
We know that:
- a + b = -8
- ab = -40
We can solve for a and b by substituting -8 - a for b in the second equation and solving for a:
a * (-8 - a) = -40
-8a - a^2 = -40
a^2 + 8a - 40 = 0
Using the quadratic formula or factoring, we can solve for a:
a = (-8 ± sqrt(8^2 - 4 * 1 * (-40))) / (2 * 1)
a = (-8 ± sqrt(256)) / 2
a = (-8 ± 16) / 2
a = -4 or a = -10
If we substitute these values for a in the equation a + b = -8, we get:
-4 + b = -8 or -10 + b = -8
b = -8 + 4 or b = -8 + 10
b = -4 or b = 2
Therefore, the two factors that make up -40 and add to -8 are -4 and 10 (or 2 and -10).