How do you factor completely #4x^3-6x^2+2x-3#?

1 Answer

Answer:

Use factoring to make the first 2 terms and the second 2 terms match, then factor them to arrive at
#(2x-3)(2x^2+1)#

Explanation:

Let's start with the original expression:

#4x^3-6x^2+2x-3#

The thing to notice here is that the first 2 terms have coefficients of 4 and -6 and the second 2 terms have coefficients of 2 and -3. We can factor out #2x^2# from the first 2 terms to have it match to the second 2 terms, like this:

#2x^2(2x-3)+(2x-3)#

We can then factor the #2x-3# and end up with:

#(2x-3)(2x^2+1)#