Question

when the expression: 4x^4 + 24x^3 + 12x^3 + 8x is factored completely, what is the largest factor that can be factored out?

Answer 1

D. 4x

they all have at least one x, and 4 goes into all of the numbers at least once

Answer 2

Let's start by grouping like terms so we can factor out the most
(4x^4+24x^3)+(12x^2+8x)
now let's factor out as much as possible. we see all coefficients are multiples of 4, we will also factor out as high a degree of x as we can
4x^3(x+6)+4x(3x+2)
now we see that we still have a common multiple of 4x that we can remove
4x(x^2(x+6)+(3x+2))
so we find 4x is the largest value we can factor out