➕ Algebra 1 · Factoring
Factoring by Grouping flashcards
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All 15 flashcards at a glance
Card 1
When can you try factoring by grouping?
When a polynomial has four terms and no common factor for all four (take any GCF out first). It works if the two pairs leave the same binomial.
Card 2
Factor x3 + 9x2 + 2x + 18.
(x + 9)(x2 + 2). The pairs give x2(x + 9) + 2(x + 9).
Card 3
Factor x3 − 8x2 − 3x + 24.
(x − 8)(x2 − 3). The pairs give x2(x − 8) − 3(x − 8).
Card 4
Take a negative GCF out of −4x + 20.
−4(x − 5). Check: (−4)(x) = −4x and (−4)(−5) = +20.
Card 5
Factor 4x3 + 8x2 + x + 2.
(x + 2)(4x2 + 1). The second pair x + 2 has GCF 1, so it is 1(x + 2).
Card 6
Is y2(y + 6) + 5(y + 6) written as a product of factors?
No. It is a sum of two terms. Pull out the common binomial to get the product (y + 6)(y2 + 5).
Card 7
Rearrange and factor ab + 6 + 2a + 3b.
Reorder as ab + 3b + 2a + 6. Then b(a + 3) + 2(a + 3) = (a + 3)(b + 2).
Card 8
How do you check a factoring answer?
Expand it. Multiplying the factors must give back the original polynomial (the terms may appear in a different order).
Card 9
What do you do first if all four terms share a GCF?
Take it out front, then group the polynomial left inside the parentheses. Keep the GCF in the final answer.
Card 10
In this lesson’s “Great Pairs Match Exactly” trick, what do G, P, M and E stand for?
G: take out the GCF of all four terms first. P: Pair the terms and take out each pair’s GCF. M: the leftover binomials must Match (fix signs if needed). E: Extract the common binomial, then Expand to check.
Card 11
Split the middle term and factor 5x2 + 11x + 2.
a × c = 10 and 1 + 10 = 11, so 5x2 + x + 10x + 2 = x(5x + 1) + 2(5x + 1) = (5x + 1)(x + 2).
Card 12
To split the middle term of ax2 + bx + c, what two numbers do you look for?
Two integers m and n with m × n = a × c and m + n = b. Then rewrite bx as mx + nx and group.
Card 13
What happens when no two integers have product a × c and sum b, as in 3x2 + 2x + 5?
If any GCF is already out, the trinomial is prime. Here there is no GCF, a × c = 15, and the integer pairs with that product add up to 16, 8, −16 or −8, never 2.
Card 14
If the two leftover binomials do not match, what can you try?
First check the sign of each GCF you took out (you may need a negative). Then try rearranging the terms. If nothing matches, grouping does not work. That does not prove the polynomial is prime.
Card 15
Why is (x − 7) not the same binomial as (7 − x)?
They are opposites: 7 − x = −(x − 7). Take out a −1 to make them match.