Question

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

Answer 1

We are dividing the polynomial $2x^{2} +13x+26$ by x+4

notice that $2x^{2}$ is x times 2x,

so if we multiply (x+4) by 2x, which gives us $2 x^{2} +8x$, we can 'separate' one $2 x^{2} +8x$ from $2x^{2} +13x+26$  to get the following simplification:

$\frac{2x^{2} +13x+26}{x+4}= \frac{ 2x^{2}+8 x}{x+4} + \frac{5x+26}{x+4}=2x+ \frac{5x+26}{x+4}$

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 

$\frac{5x+26}{x+4}= \frac{5x+20}{x+4}+ \frac{6}{x+4}=5+\frac{6}{x+4}$

$\frac{6}{x+4}$ can not be simplified any further since the degree of 6, is smaller than the degree of x+4

combining our work, we have:

$\frac{2x^{2} +13x+26}{x+4}=2x+5+\frac{6}{x+4}$

Answer:

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.

Answer 2

Answer:

Q(x)= 2x+5

R(x)= 6

Step-by-step explanation: