Question

Rewrite (2x^2+13x+26) / x+4 in the form q(x)+r(x)/b(x) . Then find q(x) and r(x). In the rewritten expression, q(x) is_____and r(x) is______ .
#1 a.)x+a , b.)2x+5 , c.)2x+13
#2 a.)0 , b.)6 , c.)226
ive been stuck on this for 15 mins and i need help plz

Answer 1

The value of q(x) is $2 x+5$

The value of r(x) is $6$

Explanation:

The given expression is $\frac{2 x^{2}+13 x+26}{x+4}$

We need to rewrite the expression in the form of $q(x)+\frac{r(x)}{b(x)}$

Simplifying the expression, we get,

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

Separating the fractions, we have,

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

$2 x+\frac{5 x+26}{x+4}$  -----------(1)

Now, we shall further simplify the term $\frac{5 x+26}{x+4}$ , we get,

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

Common out 5 from the numerator, we have,

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

Substituting the value $\frac{5 x+26}{x+4}=5+\frac{6}{x+4}$ in the equation(1), we get,

$2 x+5+\frac{6}{x+1}$

Thus, the expression $\frac{2 x^{2}+13 x+26}{x+4}=2 x+5+\frac{6}{x+1}$ is in the form of $q(x)+\frac{r(x)}{b(x)}$

Hence, we have,

$q(x)=2 x+5$

$r(x)=6$ and

$b(x)=x+4$