Find the product of (4x - 3)(2x^2 - 7x + 1)a. 8x^3 - 22x^2 + 17x - 3b. 8x^3 + 8x^2 + 4x - 3c. 8x^3 - 34x^2 + 25x - 3d. 8x^3 - 42x^2 + 25x - 3

You can multiply this out the long way using the distributive property:
.. (4x -3)*(2x^2 -7x +1)
.. = 4x*(2x^2 -7x +1) -3(2x^2 -7x +1)
.. = 8x^3 -28x^2 +4x -6x^2 +21x -3
.. = 8x^3 -34x^2 +25x -3 . . . . . . . . . . . . selection C


Or you can recognize that the product will be a cubic with terms x^3 down to a constant.
The coefficient of x^3 can only come from 4x*2x^2 = 8x^3
The coefficient of x^2 will come from -3*2x^2 and 4x*-7x = (-6 -28)x^2 = -34x^2
This is sufficient to identify answer C as the correct choice.

If you want to continue,
The coefficient of x will come from -3*-7x and 4x*1 = (21 +4)x = 25x
The constant will come from -3*1 = -3.
All this arithmetic can be done in your head, so you can write down the answer without any intermediate "work", if you want to.

From a test-taking point of view, you can identify that the x^2 term will tell you the correct answer. You only need to calculate that one.