Please solve this for me....
Answers
Your input: find
2x3+7x2+2x−5
2x+4
using long division.
Write the problem in the special format:
2x+4 2x3 +7x2 +2x −5
Step 1
Divide the leading term of the dividend by the leading term of the divisor:
2x3
2x
=x2.
Write down the calculated result in the upper part of the table.
Multiply it by the divisor: x2(2x+4)=2x3+4x2.
Subtract the dividend from the obtained result: (2x3+7x2+2x−5)−(2x3+4x2)=3x2+2x−5.
x2
2x+4 2x3 +7x2 +2x −5
2x3
2x
=x2 − 2x3 +4x2 3x2 +2x −5 x2(2x+4)=2x3+4x2
Step 2
Divide the leading term of the obtained remainder by the leading term of the divisor:
3x2
2x
=
3x
2
.
Write down the calculated result in the upper part of the table.
Multiply it by the divisor:
3x
2
(2x+4)=3x2+6x.
Subtract the remainder from the obtained result: (3x2+2x−5)−(3x2+6x)=−4x−5.
x2 +
3x
2
2x+4 2x3 +7x2 +2x −5 − 2x3 +4x2 3x2 +2x −5 − 3x2 +6x −4x −5
3x2
2x
=
3x
2
3x
2
(2x+4)=3x2+6x
Step 3
Divide the leading term of the obtained remainder by the leading term of the divisor:
−4x
2x
=−2.
Write down the calculated result in the upper part of the table.
Multiply it by the divisor: −2(2x+4)=−4x−8.
Subtract the remainder from the obtained result: (−4x−5)−(−4x−8)=3.
x2 +
3x
2
−2 2x+4 2x3 +7x2 +2x −5 − 2x3 +4x2 3x2 +2x −5 − 3x2 +6x −4x −5 − −4x −8 3
−4x
2x
=−2 −2(2x+4)=−4x−8
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 +
3x
2
−2 Hints 2x+4 2x3 +7x2 +2x −5
2x3
2x
=x2 − 2x3 +4x2 3x2 +2x −5 − 3x2 +6x −4x −5 − −4x −8 3 x2(2x+4)=2x3+4x2
3x2
2x
=
3x
2
3x
2
(2x+4)=3x2+6x
−4x
2x
=−2 −2(2x+4)=−4x−8
Therefore,
2x3+7x2+2x−5
2x+4
=x2+
3x
2
−2+
3
2x+4
Answer:
2x3+7x2+2x−5
2x+4
=x2+
3x
2
−2+
3
2x+4
Related Note: Polynomial Long Division