in algebra Write the polynomial in factored form. Please show your work or explain your reasoning x^3 - 5x² + 6x
To factor the polynomial x^3 - 5x^2 + 6x, we will look for common factors and then apply the factoring techniques.
First, observe that all the terms have an x in common. So, we can factor out an x from each term:
x(x^2 - 5x + 6)
Next, we need to factor the quadratic expression (x^2 - 5x + 6). We look for two numbers that multiply to 6 (the constant term) and add to -5 (the coefficient of the x term).
The two numbers that satisfy this condition are -2 and -3. Therefore, we can factor the quadratic expression as follows:
x(x - 2)(x - 3)
Therefore, the factored form of the polynomial x^3 - 5x^2 + 6x is x(x - 2)(x - 3).