Factor t^(1/2) + 6t^(-1/2) -t^(-3/2) - 6t^(-5/2) completely so that factors of two or more terms contain no negative exponents or fractional coefficients?
1 Answer
Feb 9, 2018
Explanation:
"take out a "color(blue)"common factor of "t^(-5/2)
rArrt^(-5/2)(t^3+6t^2-t-6)
color(red)"factorise "t^3+6t^2-t-6
"note the coefficients "1+6-1-6=0
rArr(t-1)" is a factor"
"divide "t^3+6t^2-t-6" by "(t-1)
color(red)(t^2)(t-1)color(magenta)(+t^2)+6t^2-t-6
=color(red)(t^2)(t-1)color(red)(+7t)(t-1)color(magenta)(+7t)-t-6
=color(red)(t^2)(t-1)color(red)(+7t)(t-1)color(red)(+6)(t-1)cancel(color(magenta)(+6))cancel(-6)
rArr(t^3+6t^2-t-6)/(t-1)=t^2+7t+6
rArrt^(1/2)+6t^(-1/2)-t^(-3/2)-6t^(-5/2)
=t^(-5/2)(t-1)(t^2+7t+6)
=t^(-5/2)(t-1)(t+1)(t+6)
