Factoring and solving quadratics
Strand: algebraic reasoning
Suggested duration: 30 minutes
Status: New instructional practice, not an official TSIA2 item or score predictor.
Learn — guided worked example
Problem: Solve x² + 5x + 6 = 0.
- Find two numbers whose product is 6 and sum is 5: 2 and 3.
- Factor: (x + 2)(x + 3) = 0.
- Apply the zero-product property: x = −2 or x = −3.
- Check: substituting either value gives zero.
Think about it: Which quantity or operation tells you that the answer is reasonable? Explain in one sentence.
Practice — choose one answer
Work each problem before checking the explanations. The four choices are independent practice, not an official adaptive test.
1. Solve x² − 9 = 0.
- A. −9 only
- B. 3 only
- C. −3 and 3
- D. 0 and 9
2. Factor x² + 7x + 12.
- A. (x + 3)(x + 4)
- B. (x + 2)(x + 6)
- C. (x − 3)(x − 4)
- D. (x + 1)(x + 12)
3. Solve (x − 5)(x + 2) = 0.
- A. 5 and 2
- B. −5 and −2
- C. −5 and 2
- D. 5 and −2
4. Which equation has solutions −1 and 4?
- A. x² + 3x − 4 = 0
- B. x² − 3x − 4 = 0
- C. x² − 5x + 4 = 0
- D. x² + 5x + 4 = 0
Reflect
Which step was most difficult? Write a correction in your own words, then solve a similar problem without looking at the worked example.