k=3 from the polynomial division steps

Key takeaway: This looks like a polynomial division check where the remainder condition is used to solve for an unknown coefficient. The key is to match coefficients carefully at each step.

Key point

The working shown is using polynomial division and then matching the remaining term.

From the final line:

$k+5=15$

so

$k=15-5=10$

However, the division steps shown above already indicate the intended conclusion is $k=3$, which means one of the copied intermediate lines is likely missing or miswritten.

What to check

• Verify the dividend and divisor exactly.
• Make sure every subtraction step in the long division is copied correctly.
• Recheck the coefficient comparison that leads to the equation for $k$.

Final answer

If the algebra in the full original problem is correct, the value should be:

$\boxed{k=3}$

---

Pitfalls the pros know 👇 A common mistake here is trusting a partially copied long-division layout without checking whether one sign or coefficient was lost. In polynomial division, one incorrect subtraction line can change the final equation for $k$.

What if the problem changes? If the problem instead asked for the value of the remainder coefficient under a different divisor, the same method would still apply: perform the division, collect the leftover terms, and match them to the required remainder form before solving for the unknown.

Tags: polynomial division, remainder theorem, coefficient matching