Question

Factored completely, the expression 3x3 – 33x2 + 90x is equivalent to

Option 1: 3x(x2 – 33x + 90)
Option 2: 3x(x2 - 11x + 30)
Option 3: 3x(x + 5)(x + 6)
Option 4: 3x(x - 5)(x - 6)

Answer 1

To factor the expression 3x^3 - 33x^2 + 90x completely, we can start by factoring out the greatest common factor, which is 3x. This gives us 3x(x^2 - 11x + 30). Then, we factor the quadratic expression inside the parentheses as (x - 5)(x - 6).

Step-by-step explanation:

To factor the expression 3x^3 - 33x^2 + 90x completely, we can start by factoring out the greatest common factor, which is 3x. This gives us: 3x(x^2 - 11x + 30). Now we need to factor the quadratic expression in parentheses. We can find two numbers that add up to -11 and multiply to 30. Those numbers are -5 and -6. So, we can factor the quadratic expression as follows: x^2 - 11x + 30 = (x - 5)(x - 6). Therefore, the completely factored form of the given expression is 3x(x - 5)(x - 6).