Write the polynomial in factored form. Please show your work or explain your reasoning
x^3 - 5x² + 6x
explain
To factor the given polynomial, we can first look for any common factors. In this case, the only common factor is x. Factoring out an x from each term, we get:
x(x² - 5x + 6)
Next, we need to factor the quadratic expression in parentheses. To do this, we need to find two numbers that multiply to 6 and add up to -5 (the coefficient of x). The numbers that satisfy these conditions are -2 and -3.
So, the factored form of the polynomial is:
x(x - 2)(x - 3)