The calculator will divide
x3+7x2+1 by
x−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):
x−1x3+7x2+0x+1
Step 1
Divide the leading term of the dividend by the leading term of the divisor: xx3=x2.
Write down the calculated result in the upper part of the table.
Multiply it by the divisor: x2(x−1)=x3−x2.
Subtract the dividend from the obtained result: (x3+7x2+1)−(x3−x2)=8x2+1.
x−1x2x3−x3x3+7x2−x28x2+0x+0x+1+1xx3=x2x2(x−1)=x3−x2Step 2
Divide the leading term of the obtained remainder by the leading term of the divisor: x8x2=8x.
Write down the calculated result in the upper part of the table.
Multiply it by the divisor: 8x(x−1)=8x2−8x.
Subtract the remainder from the obtained result: (8x2+1)−(8x2−8x)=8x+1.
x−1x2x3−x3x3+8x+7x2−x28x2−8x28x2+0x+0x−8x8x+1+1+1x8x2=8x8x(x−1)=8x2−8xStep 3
Divide the leading term of the obtained remainder by the leading term of the divisor: x8x=8.
Write down the calculated result in the upper part of the table.
Multiply it by the divisor: 8(x−1)=8x−8.
Subtract the remainder from the obtained result: (8x+1)−(8x−8)=9.
x−1x2x3−x3x3+8x+7x2−x28x2−8x28x2+8+0x+0x−8x8x−8x8x+1+1+1−89x8x=88(x−1)=8x−8Since the degree of the remainder is less than the degree of the divisor, we are done.
The resulting table is shown once more:
x−1x2x3−x3x3+8x+7x2−x28x2−8x28x2+8+0x+0x−8x8x−8x8x+1+1+1−89Hintsxx3=x2x2(x−1)=x3−x2x8x2=8x8x(x−1)=8x2−8xx8x=88(x−1)=8x−8Therefore, x−1x3+7x2+1=(x2+8x+8)+x−19.
Answer
x−1x3+7x2+1=(x2+8x+8)+x−19A