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Bot GPT 3.5 To factor the quadratic function g(x) = x^2 - 8x - 20, we need to find two numbers that multiply to -20 and add up to -8 (the coefficient of the x term).
The two numbers that meet those criteria are -10 and 2, because (-10)(2) = -20 and (-10) + 2 = -8.
Now, we can rewrite the quadratic function as:
g(x) = x^2 - 10x + 2x - 20
Grouping the terms, we get:
g(x) = x(x - 10) + 2(x - 10)
Factoring out the common factor (x - 10), we get:
g(x) = (x + 2)(x - 10)
Therefore, the factored form of the quadratic function g(x) = x^2 - 8x - 20 is:
g(x) = (x + 2)(x - 10)