Here's the method for x² − 5x + 6 = 0, which factoring handles neatly.
Step 1: Find two numbers that multiply to +6 and add to −5. Both must be negative, since the product is positive and the sum is negative. Trying pairs: −1 and −6 multiply to 6 but add to −7, no good. −2 and −3 multiply to 6 and add to −5. Those are the numbers.
Step 2: Write the expression as two brackets: (x − 2)(x − 3) = 0.
Step 3: A product is zero only when one factor is zero, so either x − 2 = 0 or x − 3 = 0. That gives x = 2 or x = 3.
Check by substituting: for x = 2, 4 − 10 + 6 = 0; for x = 3, 9 − 15 + 6 = 0. Both work.
A tip for your daughter: the pair of numbers is the part that trips most students up. Writing out the factor pairs of the constant term (here 6: 1×6, 2×3) and checking which pair's sum matches the middle coefficient makes it systematic. If she gets stuck on a different quadratic where the numbers don't come out whole, the quadratic formula always works, and her teacher can show her how to use it.
