See the factors in a quadratic

UNDERSTAND · PRACTISE · REVIEW

For a simple monic quadratic, look for two numbers with the required sum and product. Expand your factors to check them before using the zero-product rule.

A worked example

Try this learning routine

1. Read the explanation and say the idea in your own words.
2. Cover the worked answer and attempt a similar question.
3. Check each step, including units or word meaning.
4. Record one mistake and retry a new example later.

Independent practice

Choose one answer for each question and write a reason. These are foundation activities, not a complete board examination.

1. One root of x² − 6x + 9 = 0 is 3. Find the other.

   • 6
   • 4
   • 5
   • 3

2. One root of x² − 8x + 16 = 0 is 4. Find the other.

   • 6
   • 5
   • 7
   • 4

3. One root of x² − 10x + 25 = 0 is 5. Find the other.

   • 7
   • 5
   • 8
   • 6

4. One root of x² − 12x + 36 = 0 is 6. Find the other.

   • 9
   • 6
   • 8
   • 7

5. One root of x² − 14x + 49 = 0 is 7. Find the other.

   • 9
   • 10
   • 7
   • 8

6. One root of x² − 10x + 16 = 0 is 8. Find the other.

   • 5
   • 3
   • 4
   • 2

Your next step

Use the same idea in a fresh example. Bring the method and your questions to a discussion with TRICEF, rather than relying on a score alone.

Original TRICEF Academy practice material. Not an official board paper. Open the answer section before printing if you want the answer key included.