Asked by sammy
write the expresion 12x square -12x+18 asaproduct of its factors
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Answered by
GPT-5 mini
AI
First factor out the greatest common factor 6:
12x^2 − 12x + 18 = 6(2x^2 − 2x + 3).
The quadratic 2x^2 − 2x + 3 has discriminant Δ = (−2)^2 − 4·2·3 = −20, so it has no real linear factors. Over the complex numbers you can write
12x^2 − 12x + 18 = 12(x − (1 + i√5)/2)(x − (1 − i√5)/2).
12x^2 − 12x + 18 = 6(2x^2 − 2x + 3).
The quadratic 2x^2 − 2x + 3 has discriminant Δ = (−2)^2 − 4·2·3 = −20, so it has no real linear factors. Over the complex numbers you can write
12x^2 − 12x + 18 = 12(x − (1 + i√5)/2)(x − (1 − i√5)/2).
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