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Simplify algebraic fractions by factorising

10th grade (Year 11 in England) · 16 questions · Common Core: HSA.APR.D.6, HSA.SSE.A.2 · England: GCSE Higher Algebra

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Score/ 16

1
Question 1
Simplify: (x² + 10x + 21)/(x + 3)
- A. (x + 7)
- B. (x + 10)
- C. (x + 21)
- D. (x − 7)
2
Question 2
Ben simplified (x + 8)/x by crossing out the x's and got 1 + 8 = 9. Is this right?
- A. Right
- B. Wrong: only common factors can be cancelled, not terms
- C. Right, but only when x is positive
3
Question 3
Simplify: (x² − 3x − 10)/(x − 5)
- A. (x − 3)
- B. (x − 2)
- C. (x + 2)
- D. (x − 10)
4
Question 4
Mateo simplified (x + 2)/x by crossing out the x's and got 1 + 2 = 3. Is this right?
- A. Right
- B. Wrong: only common factors can be cancelled, not terms
- C. Right, but only when x is positive
5
Question 5
Simplify: (x² − 49)/(x + 7)
- A. 1/(x − 7)
- B. (x − 7)
- C. (x² − 7)
- D. (x + 7)
6
Question 6
Fatima simplified (x + 8)/x by crossing out the x's and got 1 + 8 = 9. Is this right?
- A. Right
- B. Wrong: only common factors can be cancelled, not terms
- C. Right, but only when x is positive
7
Question 7
Simplify: (x² + 4x − 21)/(x + 7)
- A. (x − 3)
- B. (x − 21)
- C. (x − 3)/(x + 7)
- D. (x + 3)
8
Question 8
Omar simplified (x + 2)/x by crossing out the x's and got 1 + 2 = 3. Is this right?
- A. Right
- B. Wrong: only common factors can be cancelled, not terms
- C. Right, but only when x is positive
9
Question 9
Simplify: (x² − 3x − 4)/(x² − 16)
- A. (x + 1)/(x − 4)
- B. (x + 1)/(x + 4)
- C. (x − 1)/(x + 4)
- D. (x − 4)/(x + 4)
10
Question 10
Zara simplified (x + 2)/x by crossing out the x's and got 1 + 2 = 3. Is this right?
- A. Right
- B. Wrong: only common factors can be cancelled, not terms
- C. Right, but only when x is positive
11
Question 11
Simplify: (x² − 7x + 12)/(x − 4)
- A. (x − 3)
- B. (x − 3)/(x − 4)
- C. (x − 7)
- D. (x + 3)
12
Question 12
Hana simplified (x + 5)/x by crossing out the x's and got 1 + 5 = 6. Is this right?
- A. Right
- B. Wrong: only common factors can be cancelled, not terms
- C. Right, but only when x is positive
13
Question 13
Simplify: (x² − 5x − 14)/(x + 2)
- A. (x − 7)
- B. (x − 7)/(x + 2)
- C. (x − 14)
- D. (x − 5)
14
Question 14
Kai simplified (x + 9)/x by crossing out the x's and got 1 + 9 = 10. Is this right?
- A. Right
- B. Wrong: only common factors can be cancelled, not terms
- C. Right, but only when x is positive
15
Question 15
Simplify: (x² − 2x − 35)/(x − 7)
- A. (x − 35)
- B. (x + 5)
- C. (x − 5)
- D. (x + 5)/(x − 7)
16
Question 16
Tariq simplified (x + 6)/x by crossing out the x's and got 1 + 6 = 7. Is this right?
- A. Right
- B. Wrong: only common factors can be cancelled, not terms
- C. Right, but only when x is positive

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Answer key: Simplify algebraic fractions by factorising

1. A. (x + 7)
2. B. Wrong: only common factors can be cancelled, not terms
3. C. (x + 2)
4. B. Wrong: only common factors can be cancelled, not terms
5. B. (x − 7)
6. B. Wrong: only common factors can be cancelled, not terms
7. A. (x − 3)
8. B. Wrong: only common factors can be cancelled, not terms
9. B. (x + 1)/(x + 4)
10. B. Wrong: only common factors can be cancelled, not terms
11. A. (x − 3)
12. B. Wrong: only common factors can be cancelled, not terms
13. A. (x − 7)
14. B. Wrong: only common factors can be cancelled, not terms
15. B. (x + 5)
16. B. Wrong: only common factors can be cancelled, not terms