How do you divide #(16z x ^ { 3} - 20z ^ { 4} x ^ { 7} ) \div ( 4z ^ { 2} x ^ { 5} )#?

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Answer 1 · 2017-08-30T19:59:50

#(4)/(zx^2) - 5z^2x^2#

#(16zx^3 - 20z^4x^7)/(4z^2x^5)#

Since the numerator has a term being subtracted from another, we cannot cancel yet. First, we can factor the numerator. The GCF is #4zx^3#.

#(4zx^3(4 - 5z^3x^4))/(4z^2x^5)#

We can now cancel #4#, #z#, and #x^3#.

#(cancel4cancelzcancel(x^3)(4 - 5z^3x^4))/(cancel4 cancel(z^2)^z cancel(x^5)^(x^2))#

We are left with

#(4 - 5z^3x^4)/(zx^2)#

We can now split this into

#(4)/(zx^2) - (5z^3x^4)/(zx^2)#

Canceling, we get

#(4)/(zx^2) - (5cancel(z^3)^(z^2) cancel(x^4)^(x^2))/(cancelz cancel(x^2)) #

#= (4)/(zx^2) - 5z^2x^2#