How do you evaluate #(12t ^ { 4} + 4t ^ { 3} - 3t ^ { 2} ) \div 3t ^ { 2}#?

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Answer 1 · 2017-11-20T22:58:44

See a solution process below:

First, we can rewrite this expression as:

#(12t^4 + 4t^3 - 3t^2)/(3t^2)#

We can factor #t^2# from each term in the numerator giving:

#((12t^2 * t^2) + (4t * t^2) - (3 * t^2))/(3t^2) =>#

#((12t^2 + 4t - 3)t^2)/(3t^2)#

We can now cancel common terms in the numerator and denominator:

#((12t^2 + 4t - 3)color(red)(cancel(color(black)(t^2))))/(3color(red)(cancel(color(black)(t^2)))) =>#

#(12t^2 + 4t - 3)/3#

Or, we can rewrite this as:

#(12t^2)/3 + (4t)/3 - 3/3 =>#

#4t^2 + 4/3t - 1#