What you’ll learn
Choose an appropriate quadratic-solving method.
Key idea
Zero-product property requires a product equal to zero; completing the square creates one grouped square by a balanced addition.
Zero-product reasoning requires zero right side; classify a method by its defining step without ruling out all other valid methods.
Worked example
Classify examples and non-examples for the concept 'Choose an appropriate quadratic-solving method'.
For (x-3)(x+2)=0, is zero-product property directly licensed by this displayed equality? Classify with evidence.
- Displayed (x-3)(x+2)=0 licenses setting either factor to zero.
- A trace x²+6x=-5 to (x+3)²=4 by adding 9 demonstrates completing the square.
Answer: Yes — product equals zero, so either factor may vanish.
Quick Check
Classify examples and non-examples for the concept 'Choose an appropriate quadratic-solving method'.
For (x-4)(x+8)=1, is zero-product property directly licensed by this displayed equality? Classify with evidence.