How do you divide #(4v^{3} + 12v^{2} + 16v ) \div 4v^{2}#?

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Answer 1 · 2018-05-03T11:52:25

#v+3+\frac{4}{v}#

Write it as a ratio:

#\frac{4v^3+12v^2+16v}{4v^2}#

And then split it into a sum of fractions:

#\frac{4v^3}{4v^2}+\frac{12v^2}{4v^2}+\frac{16v}{4v^2}#

Now, for each fraction, you can simplify the numeric part:

#\frac{v^3}{v^2}+\frac{3v^2}{v^2}+\frac{4v}{v^2}#

As well as the literal part:

#v+3+\frac{4}{v}#