The calculator will divide
u7 by
u2+1 using long division, with steps shown.
Related calculators:
Synthetic Division Calculator,
Long Division Calculator
Solution
Write the problem in the special format (missed terms are written with zero coefficients):
u2+1u7+0u6+0u5+0u4+0u3+0u2+0u+0
Step 1
Divide the leading term of the dividend by the leading term of the divisor: u2u7=u5.
Write down the calculated result in the upper part of the table.
Multiply it by the divisor: u5(u2+1)=u7+u5.
Subtract the dividend from the obtained result: (u7)−(u7+u5)=−u5.
u2+1u5u7−u7u7+0u6+0u6+0u5+u5−u5+0u4+0u4+0u3+0u3+0u2+0u2+0u+0u+0+0u2u7=u5u5(u2+1)=u7+u5Step 2
Divide the leading term of the obtained remainder by the leading term of the divisor: u2−u5=−u3.
Write down the calculated result in the upper part of the table.
Multiply it by the divisor: −u3(u2+1)=−u5−u3.
Subtract the remainder from the obtained result: (−u5)−(−u5−u3)=u3.
u2+1u5u7−u7u7−u3+0u6+0u6+0u5+u5−u5−−u5−u5+0u4+0u4+0u4+0u3+0u3−u3u3+0u2+0u2+0u2+0u+0u+0u+0+0+0u2−u5=−u3−u3(u2+1)=−u5−u3Step 3
Divide the leading term of the obtained remainder by the leading term of the divisor: u2u3=u.
Write down the calculated result in the upper part of the table.
Multiply it by the divisor: u(u2+1)=u3+u.
Subtract the remainder from the obtained result: (u3)−(u3+u)=−u.
u2+1u5u7−u7u7−u3+0u6+0u6+u+0u5+u5−u5−−u5−u5+0u4+0u4+0u4+0u3+0u3−u3u3−u3u3+0u2+0u2+0u2+0u2+0u+0u+0u+u−u+0+0+0+0u2u3=uu(u2+1)=u3+uSince the degree of the remainder is less than the degree of the divisor, we are done.
The resulting table is shown once more:
u2+1u5u7−u7u7−u3+0u6+0u6+u+0u5+u5−u5−−u5−u5+0u4+0u4+0u4+0u3+0u3−u3u3−u3u3+0u2+0u2+0u2+0u2+0u+0u+0u+u−u+0+0+0+0Hintsu2u7=u5u5(u2+1)=u7+u5u2−u5=−u3−u3(u2+1)=−u5−u3u2u3=uu(u2+1)=u3+uTherefore, u2+1u7=(u5−u3+u)+u2+1−u.
Answer
u2+1u7=(u5−u3+u)+u2+1−uA
