➕ Algebra 1 · Factoring
Factoring Out the Greatest Common Factor flashcards
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All 15 flashcards at a glance
Card 1
What does it mean to factor an expression, and how does it connect to the distributive property?
Rewrite it as a product. Pulling out a common factor is the distributive property run backward: ab + ac = a(b + c).
Card 2
Find the GCF of 40 and 64.
8. In prime factors, 40 = 2 · 2 · 2 · 5 and 64 = 2 · 2 · 2 · 2 · 2 · 2, so the shared part is 2 · 2 · 2 = 8.
Card 3
Find the GCF of 8m4 and 20m2.
4m2. The GCF of 8 and 20 is 4, and the lowest exponent of m is 2.
Card 4
Find the GCF of 10p3q and 15p.
5p. The GCF of 10 and 15 is 5, and the lowest exponent of p is 1. The letter q is missing from the second term, so it is not in the GCF.
Card 5
Factor 7k2 + 7k.
7k(k + 1). The second term, 7k ÷ (7k), leaves 1. Do not leave the 1 out.
Card 6
Factor 9y + 27 completely.
9(y + 3). The GCF of 9 and 27 is 9, not 3. Check: 9 · y + 9 · 3 = 9y + 27.
Card 7
Factor −5p2 − 15p by taking out the negative of the GCF.
−5p(p + 3). The GCF is 5p. Dividing by −5p gives −5p2 ÷ (−5p) = p and −15p ÷ (−5p) = 3. Check: −5p · p = −5p2 and −5p · 3 = −15p.
Card 8
What is the GCF of 4x and 9y? Can you factor anything out?
The GCF is 1, so there is nothing to pull out. The numbers 4 and 9 share only 1, and the letters are different.
Card 9
In this lesson’s PULL trick for factoring out the GCF, what do the letters stand for?
Pick the biggest number that divides every coefficient. Use each variable in every term at its lowest exponent. Leave the leftovers inside (divide each term by the GCF). Look back: distribute to check, and look inside for anything still common.
Card 10
How do you check a factoring, and what does the check not tell you?
Distribute and compare with the original. A match shows the answer is correct, but not that you took out the greatest common factor. Look inside the parentheses for another common factor.
Card 11
Factor 2m(n + 6) + 9(n + 6).
(n + 6)(2m + 9). The binomial (n + 6) is in both terms. Check: (n + 6)(2m + 9) = 2mn + 9n + 12m + 54, which matches the original expanded.
Card 12
Is 2(3x + 6) a completely factored form of 6x + 12?
No. It is correct, but 3x + 6 still has the common factor 3. The full GCF gives 6(x + 2).
Card 13
Find the quotient: 18w5 ÷ (6w2).
3w3 (assume w ≠ 0). Divide 18 by 6 to get 3, and subtract the exponents: 5 − 2 = 3.
Card 14
What is the GCF of y4, y7 and y3?
y3. Use the lowest exponent.
Card 15
The GCF is always positive. So why do we sometimes factor out a negative?
When the leading coefficient is negative, we choose to pull out the negative of the GCF so the first term inside is positive: −3t2 + 12t = −3t(t − 4). The positive-GCF form 3t(−t + 4) is also correct, but this is the usual convention.