Question2. Divide:
3. Divide:
4. Divide:
5. Divide:
Part B: Medium-Challenging Division
6. Divide:
7. Divide:
8. Divide:
9. Divide:
10. Divide:
Studdy Solution
STEP 1
Sure, let's solve each division problem step by step.
**Problem 2: Divide: **
Assumptions
1. We are given the expression .
2. We need to simplify this expression by dividing each term in the numerator by the denominator.
STEP 2
Divide each term in the numerator by the denominator .
STEP 3
Simplify each term.
1.
2.
STEP 4
Combine the simplified terms.
This is the simplified expression for Problem 2.
**Problem 3: Divide: **
STEP 5
Assumptions
1. We are given the expression .
2. We need to simplify this expression by dividing each term in the numerator by the denominator.
STEP 6
Divide each term in the numerator by the denominator .
STEP 7
Simplify each term.
1.
2.
STEP 8
Combine the simplified terms.
This is the simplified expression for Problem 3.
**Problem 4: Divide: **
STEP 9
Assumptions
1. We are given the expression .
2. We need to simplify this expression by dividing each term in the numerator by the denominator.
STEP 10
Divide each term in the numerator by the denominator .
STEP 11
Simplify each term.
1.
2.
STEP 12
Combine the simplified terms.
This is the simplified expression for Problem 4.
**Problem 5: Divide: **
STEP 13
Assumptions
1. We are given the expression .
2. We need to simplify this expression by dividing each term in the numerator by the denominator.
STEP 14
Divide each term in the numerator by the denominator .
STEP 15
Simplify each term.
1.
2.
STEP 16
Combine the simplified terms.
This is the simplified expression for Problem 5.
**Part B: Medium-Challenging Division**
**Problem 6: Divide: **
STEP 17
Assumptions
1. We are given the expression .
2. We need to perform polynomial long division to simplify this expression.
STEP 18
Perform polynomial long division of by .
1. Divide the leading term of the dividend by the leading term of the divisor to get .
2. Multiply the entire divisor by and subtract from the dividend.
3. Repeat the process with the new dividend.
STEP 19
After performing polynomial long division, the quotient is .
This is the simplified expression for Problem 6.
**Problem 7: Divide: **
STEP 20
Assumptions
1. We are given the expression .
2. We need to simplify this expression by dividing each term in the numerator by the denominator.
STEP 21
Divide each term in the numerator by the denominator .
STEP 22
Simplify each term.
1.
2.
3.
STEP 23
Combine the simplified terms.
This is the simplified expression for Problem 7.
**Problem 8: Divide: **
STEP 24
Assumptions
1. We are given the expression .
2. We need to perform polynomial long division to simplify this expression.
STEP 25
Perform polynomial long division of by .
1. Divide the leading term of the dividend by the leading term of the divisor to get .
2. Multiply the entire divisor by and subtract from the dividend.
3. Repeat the process with the new dividend.
STEP 26
After performing polynomial long division, the quotient is .
This is the simplified expression for Problem 8.
**Problem 9: Divide: **
STEP 27
Assumptions
1. We are given the expression .
2. We need to simplify this expression by dividing each term in the numerator by the denominator.
STEP 28
Divide each term in the numerator by the denominator .
STEP 29
Simplify each term.
1.
2.
3.
4.
STEP 30
Combine the simplified terms.
This is the simplified expression for Problem 9.
**Problem 10: Divide: **
STEP 31
Assumptions
1. We are given the expression .
2. We need to perform polynomial long division to simplify this expression.
STEP 32
Factor the denominator as .
STEP 33
Perform polynomial long division of by .
1. Divide the leading term of the dividend by the leading term of the divisor to get .
2. Multiply the entire divisor by and subtract from the dividend.
3. Repeat the process with the new dividend.
STEP 34
After performing polynomial long division, the quotient is .
This is the simplified expression for Problem 10.
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