# Divide (5x^4-20x^3+15x^2)/(5x^2)

5×4-20×3+15x25x2
Simplify the numerator.
Factor 5×2 out of 5×4-20×3+15×2.
Factor 5×2 out of 5×4.
5×2(x2)-20×3+15x25x2
Factor 5×2 out of -20×3.
5×2(x2)+5×2(-4x)+15x25x2
Factor 5×2 out of 15×2.
5×2(x2)+5×2(-4x)+5×2(3)5×2
Factor 5×2 out of 5×2(x2)+5×2(-4x).
5×2(x2-4x)+5×2(3)5×2
Factor 5×2 out of 5×2(x2-4x)+5×2(3).
5×2(x2-4x+3)5×2
5×2(x2-4x+3)5×2
Factor x2-4x+3 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 3 and whose sum is -4.
-3,-1
Write the factored form using these integers.
5×2((x-3)(x-1))5×2
5×2(x-3)(x-1)5×2
5×2(x-3)(x-1)5×2
Cancel the common factor of 5.
Cancel the common factor.
5×2(x-3)(x-1)5×2
Rewrite the expression.
(x2(x-3))(x-1)x2
(x2(x-3))(x-1)x2
Cancel the common factor of x2.
Cancel the common factor.
x2(x-3)(x-1)x2
Divide (x-3)(x-1) by 1.
(x-3)(x-1)
(x-3)(x-1)
Expand (x-3)(x-1) using the FOIL Method.
Apply the distributive property.
x(x-1)-3(x-1)
Apply the distributive property.
x⋅x+x⋅-1-3(x-1)
Apply the distributive property.
x⋅x+x⋅-1-3x-3⋅-1
x⋅x+x⋅-1-3x-3⋅-1
Simplify and combine like terms.
Simplify each term.
Multiply x by x.
x2+x⋅-1-3x-3⋅-1
Move -1 to the left of x.
x2-1⋅x-3x-3⋅-1
Rewrite -1x as -x.
x2-x-3x-3⋅-1
Multiply -3 by -1.
x2-x-3x+3
x2-x-3x+3
Subtract 3x from -x.
x2-4x+3
x2-4x+3
Divide (5x^4-20x^3+15x^2)/(5x^2)