Factor 12x^2(x-1)-4x(x-1)-5(x-1) and show work.
12x^2(x-1)-4x(x-1)-5(x-1)
factor out (x-1)
(12x^2 - 4x - 5)(x-1)
now factor the first term:
(2x+1)(6x-5)(x-1)
Thank you Steve.
To factor the expression 12x^2(x-1) - 4x(x-1) - 5(x-1), we can use the distributive property to simplify the equation.
Let's tackle the expression step by step:
Step 1: Distribute the terms within each parenthesis.
12x^2(x-1) becomes 12x^3 - 12x^2
-4x(x-1) becomes -4x^2 + 4x
-5(x-1) becomes -5x + 5
Now we can rewrite the equation with the simplified terms:
12x^3 - 12x^2 - 4x^2 + 4x - 5x + 5
Step 2: Combine like terms.
When combining like terms, we add or subtract the coefficients of terms with the same power of x.
In this case, we can combine the terms -12x^2 and -4x^2 to get -16x^2. Similarly, combining the terms 4x and -5x gives -x.
The equation is now simplified to:
12x^3 - 16x^2 - x + 5
Step 3: Factor out the common factor.
To factor the expression, we look for any common factors among the terms. In this case, the common factor is (x-1).
Pulling out the common factor (x-1) from each term, we get:
(x-1)(12x^2 - 16x - 1)
This is the factored form of the expression 12x^2(x-1) - 4x(x-1) - 5(x-1).
So, the factored expression is (x-1)(12x^2 - 16x - 1).