LEVEL J · MATH · PARENT GUIDE
Finding the patterns behind factoring
By the Kumon Answer Book Editorial TeamLast updated:
Help your child connect factors, expressions, and the bigger picture.
What does this guide cover?
- The quadratic formula (when factoring fails)
- The discriminant — predicting solutions before solving
- Rational expressions
- Irrational numbers and exact answers
- Advanced factoring patterns
How should we work through these examples?
Let your child try first, then walk through the steps together. Original examples in the style of the level, written for parents — never reproduced worksheets. These pair with the Math Level J: Advanced Quadratics parent guide for the full level picture.
EXAMPLE 01A parent walkthrough
Solve x² + 6x + 2 = 0 with the quadratic formula
x = (-6 ± √(36 - 8)) / 2 = (-6 ± √28) / 2.
√28 = 2√7, so x = -3 ± √7.
Two exact answers — no calculator needed.
FINAL ANSWER
x = -3 ± √7
EXAMPLE 02A parent walkthrough
What does the discriminant of x² + 2x + 5 tell us?
b² - 4ac = 4 - 20 = -16.
Negative means no real solutions.
Predict before solving — that's the discriminant's whole job.
FINAL ANSWER
No real solutions
EXAMPLE 03A parent walkthrough
Simplify (x² - 9) / (x - 3)
Factor the top: (x + 3)(x - 3) / (x - 3).
Cancel the common factor (x - 3).
x + 3, where x ≠ 3.
FINAL ANSWER
x + 3 (x ≠ 3)
Which mistakes should parents watch for?
- Dropping the ± and losing a whole solution
- Arithmetic slips inside the square root
- Cancelling terms instead of factors (only factors cancel)