find lcm of 16x^5-8x^4+x^3, 4x^2-x, x^2

Question

how do i solve and show work for this problem?

Answer 1

16x^5 - 8x^4 + x^3

x^3(16x^2 - 8x + 1)

x^3(4x -1)(4x-1)

.

4x^2 - x

x(4x - 1)

.

x^2 = x * x

.

For the x's (the ones by themselves) x^3 is the smallest thing that x^3, x, and x^2 go into.

For the (4x-1)'s, (4x-1)(4x-1) has enough (4x-1)'s to make (4x-1)(4x-1) or just (4x-1).

x^3(4x-1)(4x-1)

Answer:  x^3 (4x-1)^2 which is the same thing as 16x^5 - 8x^4 + x^3

Answer 2

16x^5 - 8x^4 + x^3 = x^3 (16x^2 - 8x + 1) = x^3 (4x-1) (4x-1)

4x^2 - x = x (4x-1)

x^2 = x * x

Have to have x^3 because you can factor out an x^3 or an x^2 or just an x from x^3.

Have to have (4x-1) (4x-1) because you can factor out (4x-1) (4x-1) or just (4x-1) from (4x-1) (4x-1).

Answer:  x^3 (4x-1)^2

. . . which is the same thing as 16x^5 - 8x^4 + x^3.  The other things (4x^2 - x and x^2) all divide evenly into 16x^5 - 8x^4 + x^3.