GRADE 10 · ALBERTAOUTCOME AN5
L4 · Factoring out a common factor
Learning goal
“I can find the greatest common factor of a polynomial's terms - number and variable parts - factor it out completely, and verify the factorization by expanding.”
Common factor — a factor shared by EVERY term of a polynomial (3x divides both 6x^2 and 9x, so 3x is a common factor of 6x^2 + 9x).
Greatest common factor (GCF) — the largest common factor: greatest number part, and each variable to the LOWEST power that appears in every term.
Factored form — a polynomial rewritten as a product: factor x (what remains).
Fully factored (for this lesson) — the GCF is outside and the bracket that remains has no common factor left in its terms.
Worked example
Factor 6x^2 + 9x. Step 1: Number parts 6 and 9 -> GCF 3. Variable parts x^2 and x -> the lower power, x, appears in both -> x. GCF = 3x. Step 2: Divide each term by 3x: 6x^2 / 3x = 2x; 9x / 3x = 3. Step 3: 6x^2 + 9x = 3x(2x + 3). Step 4: Verify by expanding (L1 skill): 3x*2x + 3x*3 = 6x^2 + 9x.
Check yourself — explain it
In 6x^2 + 9x, why is the GCF 3x and not 3x^2?
Paired problem — example still visible
Factor 8a^2 - 12a -> 4a(2a - 3) (GCF 4a; 8a^2 / 4a = 2a; -12a / 4a = -3)
Faded completion — last step is yours
"10x^3 + 15x^2 = 5x^2(___ + ___)" -> 2x, 3 (10x^3 / 5x^2 = 2x; 15x^2 / 5x^2 = 3)
Ready to practise?
10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.