Question 754493
let the distance be {{{d}}}, the speed {{{s}}}, and the time {{{t}}}

{{{d=st}}}...solve for {{{t}}}

{{{t=d/s}}}

if the distance traveled by a car is described as {{{d=(x^3 + 3x^2 + 5x + 3) mil}}} and its rate or speed is {{{s=(x + 1)(mil/h)}}}, then

{{{t=((x^3 + 3x^2 + 5x + 3)cross(mil))/(x + 1)(cross(mil)/h)}}}


{{{t=((x^3 + 3x^2 + 5x + 3)/(x + 1))h}}}....factor numerator

{{{x^3 + 3x^2 + 5x + 3}}}.....write {{{5x}}} as {{{3x+2x}}}


{{{(x^3+x^2)+(2x^2+2x)+(3x+3)}}}...group


{{{x^2(x+1)+2x(x+1)+3(x+1)}}}


{{{(1+x)(x^2+2x+3)}}}......plug it in {{{t=((x^3 + 3x^2 + 5x + 3)/(x + 1))h}}}


{{{t=((1+x)(x^2+2x+3))/(x + 1))h}}}....reduce


{{{t=(cross((1+x))(x^2+2x+3))/cross((x + 1)))h}}}


{{{t=(x^2+2x+3)h}}}