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Polynomials and factoring
Can do: Multiplies and factors polynomials, including differences of squares and trinomials.
Why it matters
Factoring is the technique the rest of algebra rests on — solving quadratics, simplifying rationals, everything after.
What it looks like when it's wobbly
Factors by trial and error with no systematic approach, and misses a common factor first.
⏱️ Two-minute check
"Factor x² − 9, x² + 7x + 12, and 3x² − 12x."
Solid looks like: All three, with the common factor taken out first in the last one.
The full activity for this topic · 25 minutes
Always Look for the Common Factor First
- 1Fix the order: common factor, then pattern (difference of squares), then trinomial.
- 2Use an area rectangle to see why (x + 3)(x + 4) expands as it does.
- 3For trinomials, find two numbers multiplying to c and adding to b — systematically, listing factor pairs.
- 4Always check by expanding back.
- 5Do a mixed set so they have to choose the method, not just apply the one from the lesson.
If it's too hard
Difference of squares and simple trinomials with a = 1.
If it's too easy
Trinomials with a leading coefficient, and factoring by grouping.
Say this
"Common factor first, always. Check by multiplying back out — that's free marks."