Algebraic expressions · Ages 13–14
Comparing coefficients worksheet
Part of: Polynomials & identities
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Comparing coefficients worksheet
Algebraic expressions · Ages 13–14
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.If px2 + 4x + r ≡ 7x2 + qx + 6, then p = , q = and r = .
Fill in each blank
Answer:
2.If (x + 5)(x + k) ≡ x2 + 8x + 15, then k = .
Answer:
3.If (x + 3)(x + k) ≡ x2 + 6x + 9, then k = .
Answer:
4.If px2 + 6x + r ≡ 5x2 + qx + 16, then p = , q = and r = .
Fill in each blank
Answer:
5.If (x − 3)(x + k) ≡ x2 + mx − 27, then k = and m = .
Fill in each blank
Answer:
6.If (x + 8)(x + k) ≡ x2 + mx − 56, then k = and m = .
Fill in each blank
Answer:
7.If A(x + 7) + B(x − 2) ≡ 3x + 30, then A = and B = .
Fill in each blank
Answer:
8.If 6x2 + bx + 32 ≡ (6x + 8)(x + 4), then b = .
Answer:
9.If A(x + 8) + B(x − 6) ≡ −5x + 44, then A = and B = .
Fill in each blank
Answer:
Part B: Choose, or true or false (2 marks each)
10.If (x + 6)(x + 5) ≡ x2 + px + q, then p = 11 and q = 11.
True or false?
Answer:
11.If (px + 8)(x + 9) ≡ 3x2 + qx + 72, what are p and q?
- A. p = 3, q = 35
- B. p = 72, q = 35
- C. p = 3, q = 33
- D. p = 3, q = 17
Choose the right answer
Answer:
12.If (x + 1)(x + 5) ≡ x2 + px + q, then p = 6 and q = 5.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.If (x + p)(x + q) ≡ x2 + 9x + 14 and p > q, then p = and q = .
Fill in each blank
Working:
Answer:
14.If 3(x + h)2 + k ≡ 3x2 + 30x + 82, then h = and k = .
Fill in each blank
Working:
Answer:
15.Given (x + 8)(x + k) ≡ x2 + mx + 48. (a) Comparing constants, k = ; (b) comparing x's coefficients, m = .
Fill in each blank
Working:
Answer:
16.If (x + 2)(px + q) ≡ 5x2 + 5x − 10, what are p and q?
- A. p = 5, q = 5
- B. p = 5, q = −10
- C. p = 2, q = −5
- D. p = 5, q = −5
Choose the right answer
Working:
Answer:
17.If 2x2 + kx − 21 ≡ (2x − 3)(x + 7), then k = .
Working:
Answer:
18.If 6x + 5 ≡ p(x + 1) + q, then p = 6 and q = 5.
True or false?
Working:
Answer:
Show the answers and working
Comparing coefficients worksheet: Answers and working
Part A: Working out and filling in
1. 7, 4, 6
In an identity, like terms' coefficients match: x2's, p = 7; x's, q = 4; the constants, r = 6.
2. 3
The left is x2 + (5 + k)x + 5k. Comparing x's coefficients, 5 + k = 8, so k = 3; the constant 5 × 3 = 15 agrees.
3. 3
The left is x2 + (3 + k)x + 3k. Comparing x's coefficients, 3 + k = 6, so k = 3; the constant 3 × 3 = 9 agrees.
4. 5, 6, 16
In an identity, like terms' coefficients match: x2's, p = 5; x's, q = 6; the constants, r = 16.
5. 9, 6
The left is x2 + ((−3) + k)x + (−3)k. Comparing constants, (−3)k = −27, so k = 9; comparing x's coefficients, m = (−3) + (9) = 6.
6. −7, 1
The left is x2 + ((8) + k)x + (8)k. Comparing constants, (8)k = −56, so k = −7; comparing x's coefficients, m = (8) + (−7) = 1.
7. 4, −1
The left is (A + B)x + (7A − 2B). Comparing x's coefficients, A + B = 3; comparing constants, 7A − 2B = 30. Solving the two gives A = 4, B = −1.
8. 32
The right is 6x2 + 24x + 8x + 32 = 6x2 + 32x + 32. Comparing x's coefficients, b = 32.
9. 1, −6
The left is (A + B)x + (8A − 6B). Comparing x's coefficients, A + B = −5; comparing constants, 8A − 6B = 44. Solving the two gives A = 1, B = −6.
Part B: Choose, or true or false
10. False
The left is x2 + 11x + 30. Comparing coefficients: p = 11, q = 30.
11. A. p = 3, q = 35
The left is px2 + (p × 9 + 8)x + 72. Comparing x2's coefficients, p = 3; comparing x's, q = 3 × 9 + 8 = 35.
12. True
The left is x2 + 6x + 5. Comparing coefficients: p = 6, q = 5.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 7, 2
The left is x2 + (p + q)x + pq. Comparing: p + q = 9 and pq = 14. The two numbers with sum 9 and product 14 are 7 and 2.
14. 5, 7
The left is 3x2 + 3(2h)x + 3h2 + k. x's coefficients: 2 × 3 × h = 30, h = 5; constants: 3 × (5)2 + k = 82, k = 7.
15. 6, 14
The left is x2 + (8 + k)x + 8k. (a) 8k = 48, so k = 6; (b) m = 8 + 6 = 14.
16. D. p = 5, q = −5
The left is px2 + (q + 2p)x + 2q. x2's coefficients: p = 5; constants: 2q = −10, q = −5; x's coefficient −5 + 2 × 5 = 5 agrees.
17. 11
The right is 2x2 + 14x − 3x − 21. Comparing x's coefficients: k = 14 − 3 = 11.
18. False
The right is px + (p + q). x's coefficients: p = 6; constants: p + q = 5, so q = 5 − 6 = −1.
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