Grade 10 — Mathematics 10C › C10U06 Polynomials: Multiply & Factor

Grade 10 › C10U06 Polynomials: Multiply & Factor › L8
GRADE 10 · ALBERTAOUTCOME AN5

L8 · Factoring strategies clinic

Learning goal

“I can factor any polynomial from this unit by running the strategy in order - common factor first, then count terms and choose the pattern - factor in stages when needed, and verify the complete factorization by expanding.”

Strategy order — the fixed checklist: (1) GCF first, always; (2) count the remaining terms; (3) two terms -> difference of squares? three terms -> pair/ac hunt.
Staged factoring — factoring in more than one step, e.g. 3x^2 - 27 = 3(x^2 - 9) = 3(x - 3)(x + 3): not finished until no stage can continue.
Prime polynomial (for this unit) — a polynomial no tool in this unit factors, e.g. x^2 + x + 1 or x^2 + 25. Naming it correctly is a correct answer, not a failure.
Complete factorization — the final product form after all stages: GCF outside, every remaining factor prime for this unit's tools.
Worked example

Factor 3x^2 - 27 completely. Step 1: Checklist step 1: GCF of 3x^2 and -27 is 3 -> 3(x^2 - 9). Step 2: Not finished - the bracket has two terms and is a difference of squares: x^2 - 9 = (x - 3)(x + 3). Step 3: 3x^2 - 27 = 3(x - 3)(x + 3). Step 4: Verify by expanding the full chain: (x - 3)(x + 3) = x^2 - 9, and 3(x^2 - 9) = 3x^2 - 27.

Check yourself — explain it

A student stops at 3(x^2 - 9) and calls it complete. What test proves them wrong?

Paired problem — example still visible

Factor 5x^2 - 20 completely -> 5(x - 2)(x + 2)

Faded completion — last step is yours

"2x^2 + 12x + 18 = 2(x^2 + 6x + 9) = 2(x + ___)(x + ___)" -> 3, 3 (pair of 9 summing to 6 is 3, 3 - a repeated factor is legal)

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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