factor:
2x^3 - x^2 - 162x + 81
and could you show steps as well? thanks
Thank you
see:
http://www.jiskha.com/display.cgi?id=1303393053
To factor the given expression 2x^3 - x^2 - 162x + 81, we can use the factoring by grouping method. Here are the steps:
Step 1: Group the terms in pairs. In this case, we can group the first two terms and the last two terms:
(2x^3 - x^2) - (162x - 81)
Step 2: Factor out the greatest common factor (GCF) from each group. In the first group, the GCF is x^2:
x^2(2x - 1) - (162x - 81)
Step 3: Notice that the second group has a negative sign, so we can factor out -1 to simplify the expression:
x^2(2x - 1) - (-1)(162x - 81)
Step 4: Now we can factor out the common binomial factor (2x - 1):
x^2(2x - 1) + (-1)(162x - 81)
(2x - 1)(x^2 - 81)
Step 5: Further factor the remaining expression. The second factor is the difference of squares, so we can factor it as:
(2x - 1)(x - 9)(x + 9)
So, the factored form of 2x^3 - x^2 - 162x + 81 is (2x - 1)(x - 9)(x + 9).