Question

solve by factoring, give all the real solutions: \\(-x^3 + 4x^2 - 3x = 0\\)

give multiple solutions separated by a comma \\(x =\\)
no solutions

Explanation:

Factor out the greatest common factor

$$ -x(x^2 - 4x + 3) = 0 $$

Factor the quadratic trinomial

$$ -x(x - 1)(x - 3) = 0 $$

Apply the zero product property to find all real solutions

$$ x = 0, \quad x = 1, \quad x = 3 $$

Answer:

Solve by factoring, give all the real solutions: \(-x^3 + 4x^2 - 3x = 0\)

Give multiple solutions separated by a comma \(x =\) <blank>0, 1, 3</blank>