Question

divide. if the polynomial does not divide evenly, include the remainder as a fraction.\\((14u^{4} - 65u^{3} - 369u^{2} - 56u) \div (u - 8)\\)

Explanation:

Step1: Set up polynomial long division

Divide $14u^4$ by $u$ to get first term of quotient.
$\frac{14u^4}{u}=14u^3$

Step2: Multiply divisor by $14u^3$

Subtract result from dividend.
$14u^3(u-8)=14u^4-112u^3$
$(14u^4-65u^3-369u^2-56u)-(14u^4-112u^3)=47u^3-369u^2-56u$

Step3: Divide $47u^3$ by $u$

Get next term of quotient.
$\frac{47u^3}{u}=47u^2$

Step4: Multiply divisor by $47u^2$

Subtract result from new dividend.
$47u^2(u-8)=47u^3-376u^2$
$(47u^3-369u^2-56u)-(47u^3-376u^2)=7u^2-56u$

Step5: Divide $7u^2$ by $u$

Get next term of quotient.
$\frac{7u^2}{u}=7u$

Step6: Multiply divisor by $7u$

Subtract result from new dividend.
$7u(u-8)=7u^2-56u$
$(7u^2-56u)-(7u^2-56u)=0$

Answer:

$14u^3 + 47u^2 + 7u$