factor 2g^3-g^2-8g+4
To factor the expression 2g^3 - g^2 - 8g + 4, we can look for common factors among the terms and then use other factoring methods if necessary.
First, let's look for a common factor. The common factor in this expression is 1 because all the coefficients are 1. Therefore, we can't factor out any number.
Next, let's try to factor by grouping. Group the terms in pairs:
(2g^3 - g^2) + (-8g + 4)
Now, we can factor out the greatest common factor (GCF) from each group:
g^2(2g - 1) - 4(2g - 1)
Notice that we have a common binomial factor (2g - 1). Factor this out:
(2g - 1)(g^2 - 4)
Now, we can further factor the difference of squares g^2 - 4:
(2g - 1)(g + 2)(g - 2)
Therefore, the fully factored form of 2g^3 - g^2 - 8g + 4 is (2g - 1)(g + 2)(g - 2).