PreCalculus Honors
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Homework #15/16
Show all work on a separate piece of looseleaf paper.
Find the quotient and remainder using LONG DIVISION:
1. (4x3 – 3x2 + x + 1) ÷ (x + 2)
2. (5x4 – 3x2 + x + 1) ÷ (x2 + 2)
3. (2x4 – 3x3 + x + 1) ÷ (2x2 + x + 1)
4. (-3x4 – 2x – 1) ÷ (x – 1)
5. (x3 – a3) ÷ (x – a)
Find the quotient and remainder using SYNTHETIC DIVISION.
6. (x3 – x2 + 2x + 4) ÷ (x – 2)
7. (3x3 + 2x2 – x + 3) ÷ (x – 3)
8. (x5 – 4x3 + x) ÷ (x + 3)
9. (4x6 – 3x4 + x2 + 5) ÷ (x – 1)
10. (x5 + 1) ÷ (x + 1)
Find the quotient and remainder using the REVERSE TABULAR METHOD.
11. (2x3 + x2 – 16x + 15) ÷ (2x – 3)
12.
6𝑥 5 +4𝑥 4 −6𝑥3 +14𝑥 2 −8
6𝑥+4
13. (3x5 + 12x4 + 11x3 + 2x2 – 4x – 2) ÷ (3x2 – 1)
14. Find the sum of a, b, c, and d if
𝑥 3 −2𝑥 2 +3𝑥+5
𝑥+2
= 𝑎𝑥 + 𝑏𝑥 + 𝑐 +
𝑑
𝑥+2
Answers:
45
1. 4x2 – 11x + 23 – 𝑥+2
𝑥+27
2. 5x2 – 13 + 𝑥 2 +2
1
5𝑥+1
3. x2 – 2x + 2 + 2(2𝑥 2 +𝑥+1)
6
4. -3x3 – 3x2 – 3x – 5 – 𝑥−1
5. x2 + ax + a2
12
6. x2 + x + 4 + 𝑥−2
99
7. 3x2 + 11x + 32 + 𝑥−3
138
8. x4 – 3x3 + 5x2 – 15x + 46 – 𝑥+3
7
9. 4x5 + 4x4 + x3 + x2 + 2x + 2 + 𝑥−1
10. x4 – x3 + x2 – x + 1
11. x2 + 2x – 5
12. x4 – x2 + 3x – 2
13. x3 + 4x2 + 4x + 2
14. –9