factoring quadratics cubed. 54x^3-15x^2-6x
Always look for a greatest common factor first. Do you see one????
= 3x(18x^2 - 5x - 2)
3x(2x - 1)(9x + 2)
To factor a cubic quadratic expression like 54x^3 - 15x^2 - 6x, we need to find a common factor and then use a factoring method called grouping. Here's how you can do it step by step:
Step 1: Find the Greatest Common Factor (GCF)
In this case, we can factor out a common factor of 3x from each term:
3x(18x^2 - 5x - 2)
Step 2: Factor the quadratic expression (18x^2 - 5x - 2)
Now we need to factor the quadratic expression 18x^2 - 5x - 2. We can do this by using the factoring method called grouping:
(3x )(6x ) + (-2)(-1) (note that the middle term -5x came from the multiplication of the last terms)
Step 3: Factor by grouping
We will group the terms as follows:
(3x^2 - 2x) + (6x - 1)
Step 4: Factor out common terms from each group
From the first group, we can factor out an x:
x(3x - 2)
From the second group, we can factor out a 1:
1(6x - 1)
Step 5: Final factorization
Putting it all together, our factored quadratic expression is:
3x(3x - 2) + 1(6x - 1)
So, 54x^3 - 15x^2 - 6x can be factored as:
3x(3x - 2) + 1(6x - 1)