Final answer:
To factor the expression 2x³-3x, we identify 'x' as the greatest common factor and factor it out, leaving us with the final factored form x(2x² - 3).
Step-by-step explanation:
To factor the expression 2x³-3x completely, we need to identify the greatest common factor (GCF) that both terms share. In this case, both terms have an 'x' in common. Also, we can identify that the numerical coefficient of the second term (3) is a divisor of the numerical coefficient of the first term (2x²).
The GCF is therefore 'x', which we can factor out. This leaves us with:
x(2x² - 3)
Inside the parentheses, there is no further factoring that can be done since '2x²' and '-3' are not multiples of the same factor and do not share a common variable. The expression is now fully factored.