What is the result when you divide (-32x^3+24x^2-16x) by -4x?

Divide -4x by each term

(-32x^3 / -4x) + (24x^2 / -4x) - (16x / -4x)
= 8x^2 + -6x + 4

32 x ³ - 24 x ² + 16 x
-----------------------
4 x

8 x ² - 6 x + 4

(-32x³ + 24x² - 16x) / (-4x)

8x² - 6x + 4

(-32x^3 + 24x^2 - 16x)/-4x
= -4x(8x^2 - 6x + 4)/-4x
= (8x^2 - 6x + 4)/1
= 8x^2 - 6x + 4
= 2(4x^2 - 3x + 2)

-32x^3/-4x=8x^2
24x^2/-4x=-6x
-16x/-4x=4

8x^2 - 6x + 4

-32x^3+24x^2-16x) by -4x
means,

(-32x^3/-4x )+ (24x^2/-4x) - (16x/-4x)
Simplify each term,

(8x^2) + (-6x) - (-4)

8x^2 - 6x + 4

(-32x^3+24x^2-16x) / -4x

easiest thing is to factor out a -4x from the numerator first

(-32x³+24x²-16x)
-4x(8x²-6x+4)

so
(-32x³+24x²-16x)
-----
-4x

becomes

-4x(8x²-6x+4)
------------------
-4x

the -4x's cancel and you're left with

8x²-6x+4

8x^2 - 6x +4