Factor Completely with respect to the intergers. 2x^3-3x^2+4x-6
Try factoring out (2x-3) through grouping.
2x(x^2+2)-3(x^2+2)
To factor the given expression, 2x^3 - 3x^2 + 4x - 6, we can use a method called grouping. This involves grouping terms together and factoring out their common factors.
First, let's group the terms in pairs:
(2x^3 - 3x^2) + (4x - 6)
Now, let's factor out the greatest common factor from each group separately. From the first group, we can factor out x^2:
x^2(2x - 3)
From the second group, we can factor out 2:
2(2x - 3)
Now, notice that both groups have a common factor of (2x - 3). We can factor this out:
(2x - 3)(x^2 + 2)
Therefore, the completely factored form of the expression 2x^3 - 3x^2 + 4x - 6 is:
(2x - 3)(x^2 + 2).