Answer:
x3−12x2+38x−17x−7=x2−5x+3+4x−7 Brainliest pls???
Step-by-step explanation:
Write the problem in the special format:
x−7
x3 −12x2 +38x −17
Step 1
Divide the leading term of the dividend by the leading term of the divisor:
x3
x
=x2.
Write down the calculated result in the upper part of the table.
Multiply it by the divisor: x2(x−7)=x3−7x2.
Subtract the dividend from the obtained result: (x3−12x2+38x−17)−(x3−7x2)=−5x2+38x−17.
x2
x−7
x3 −12x2 +38x −17
x3
x
=x2
−
x3 −7x2
−5x2 +38x −17
x2(x−7)=x3−7x2
Step 2
Divide the leading term of the obtained remainder by the leading term of the divisor:
−5x2
x
=−5x.
Write down the calculated result in the upper part of the table.
Multiply it by the divisor: −5x(x−7)=−5x2+35x.
Subtract the remainder from the obtained result: (−5x2+38x−17)−(−5x2+35x)=3x−17.
x2 −5x
x−7
x3 −12x2 +38x −17
−
x3 −7x2
−5x2 +38x −17
−
−5x2 +35x
3x −17
−5x2
x
=−5x
−5x(x−7)=−5x2+35x
Step 3
Divide the leading term of the obtained remainder by the leading term of the divisor:
3x
x
=3.
Write down the calculated result in the upper part of the table.
Multiply it by the divisor: 3(x−7)=3x−21.
Subtract the remainder from the obtained result: (3x−17)−(3x−21)=4.
x2 −5x +3
x−7
x3 −12x2 +38x −17
−
x3 −7x2
−5x2 +38x −17
−
−5x2 +35x
3x −17
−
3x −21
4
3x
x
=3
3(x−7)=3x−21
Since the degree of the remainder is less than the degree of the divisor, then we are done.
The resulting table is shown once more:
x2 −5x +3
Hints
x−7
x3 −12x2 +38x −17
x3
x
=x2
−
x3 −7x2
−5x2 +38x −17
−
−5x2 +35x
3x −17
−
3x −21
4
x2(x−7)=x3−7x2
−5x2
x
=−5x
−5x(x−7)=−5x2+35x
3x
x
=3
3(x−7)=3x−21
Therefore,
x3−12x2+38x−17
x−7
=x2−5x+3+
4
x−7
Answer:
x3−12x2+38x−17
x−7
=x2−5x+3+
4
x−7
