Answer:
x ∈ {-4, 2}
Step-by-step explanation:
The x-coefficient (+2) is the sum of the constants in the binomial factors of the equation, and the constant term (-8) is their product.
Since you're familiar with the divisors of 8, you know that the two factors of -8 that total +2 are -2 and +4. These are the constants in the binomial factors:
f(x) = x^2 +2x -8
f(x) = (x -2)(x +4)
The roots of f(x) are the values of x that make these factors be zero. They are x=2 and x=-4.
The roots of f(x) are -4 and 2.
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Above is the solution by factoring. We can also "complete the square" to find the roots. Anytime we're looking for roots, we want the values of x that make f(x) = 0.
x^2 +2x -8 = 0
x^2 +2x = 8 . . . . . add the opposite of the constant
x^2 +2x +1 = 8 +1 . . . . . add the square of half the x-coefficient: (2/2)² = 1
(x +1)² = 9 . . . . . . . . . . . write as squares
x +1 = ±√9 = ±3 . . . . . . take the square root
x = -1 ± 3 . . . . . . . . . . . subtract 1
The roots are x=-4, x=2.
