Question

1. (8k^3 - 77k^2 - 26k - 35) div (k - 10)

Explanation:

Step1: Use polynomial long - division

We divide the polynomial $8k^{3}-77k^{2}-26k - 35$ by $k - 10$. First, divide the leading term of the dividend $8k^{3}$ by the leading term of the divisor $k$. The result is $8k^{2}$.
$8k^{2}(k - 10)=8k^{3}-80k^{2}$

Step2: Subtract the product from the dividend

$(8k^{3}-77k^{2}-26k - 35)-(8k^{3}-80k^{2})=3k^{2}-26k - 35$

Step3: Divide the leading term of the new dividend

Divide the leading term $3k^{2}$ of the new dividend $3k^{2}-26k - 35$ by the leading term $k$ of the divisor. The result is $3k$.
$3k(k - 10)=3k^{2}-30k$

Step4: Subtract the product from the new dividend

$(3k^{2}-26k - 35)-(3k^{2}-30k)=4k - 35$

Step5: Divide the leading term of the new dividend

Divide the leading term $4k$ of the new dividend $4k - 35$ by the leading term $k$ of the divisor. The result is $4$.
$4(k - 10)=4k-40$

Step6: Subtract the product from the new dividend

$(4k - 35)-(4k - 40)=5$

Answer:

$8k^{2}+3k + 4+\frac{5}{k - 10}$