Rewrite 2x^2+13x+26/x+4 in the form q(x)+r(x)/b(x) . then find q(x) and r(x).

We are dividing the polynomial  by x+4

notice that  is x times 2x,

so if we multiply (x+4) by 2x, which gives us , we can 'separate' one from   to get the following simplification:



similarly we notice that 5x is x times 5, so if we multiply (x+4) by 5, we get 5x+20 so we can rewrite 



can not be simplified any further since the degree of 6, is smaller than the degree of x+4

combining our work, we have:



q(x)= 2x+5
r(x)=6
b(x)=x+4

Remark: we can solve the problem by long division or the division algorithm as well.