Card 1 of 20
EasyStudy card 1
Prompt
What is factoring?
Answer
Rewriting a sum or difference as an equivalent product.
MathChapter 10: Law of Exponents and Polynomials
Flashcards
Factoring Using the Distributive Property Flashcards
Recall GCF extraction, negative factors, grouping, opposite factors, and expansion checks.
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Card 2 of 20
EasyStudy card 2
Prompt
What is the first step in GCF factoring?
Answer
Find the complete numeric and variable GCF of every term.
Card 3 of 20
EasyStudy card 3
Prompt
Which variable exponent is extracted as a GCF?
Answer
The smallest exponent shared by all terms.
Card 4 of 20
EasyStudy card 4
Prompt
What identity explains GCF factoring?
Answer
The Distributive Property used in reverse.
Formula
\[ab+ac=a(b+c)\]
Card 5 of 20
EasyStudy card 5
Prompt
Factor \(12x+18\).
Answer
\(6(2x+3)\)
Card 6 of 20
MediumStudy card 6
Prompt
Factor \(15x^4-10x^2\).
Answer
\(5x^2(3x^2-2)\)
Card 7 of 20
MediumStudy card 7
Prompt
When is extracting a negative GCF useful?
Answer
When it makes the leading term inside parentheses positive or aligns opposite factors.
Card 8 of 20
EasyStudy card 8
Prompt
What happens to inside signs when a negative factor is extracted?
Answer
Every inside sign reverses.
Card 9 of 20
MediumStudy card 9
Prompt
What is factoring by grouping designed for in this lesson?
Answer
Four-term expressions that can be paired into groups sharing an identical binomial.
Card 10 of 20
EasyStudy card 10
Prompt
What must the two partially factored groups share?
Answer
Exactly the same binomial factor after sign normalization.
Card 11 of 20
MediumStudy card 11
Prompt
Why can \(a-b\) be rewritten as \(-(b-a)\)?
Answer
They are opposite expressions; multiplying \(b-a\) by \(-1\) gives \(a-b\).
Card 12 of 20
MediumStudy card 12
Prompt
What should you try if grouped binomials differ only by reversed subtraction?
Answer
Factor \(-1\) from one group to make the binomials identical.
Card 13 of 20
EasyStudy card 13
Prompt
How do you verify a factorization conclusively?
Answer
Expand it and confirm every original term, coefficient, exponent, and sign returns.
Card 14 of 20
MediumStudy card 14
Prompt
What does an incomplete GCF look like?
Answer
The terms inside parentheses still share a nontrivial factor.
Card 15 of 20
MediumStudy card 15
Prompt
Factor \(ax+ay+bx+by\) by grouping.
Answer
\((a+b)(x+y)\)
Card 16 of 20
MediumStudy card 16
Prompt
After factoring each pair, what is factored out next?
Answer
The common binomial, leaving the two outside factors in a second binomial.
Card 17 of 20
MediumStudy card 17
Prompt
What zero-product step is available after a factored expression equals zero?
Answer
Set each factor equal to zero and solve each resulting relation.
Card 18 of 20
HardStudy card 18
Prompt
Why is a single numerical input not enough to prove two factorizations equivalent?
Answer
Different expressions can agree at one input; symbolic expansion proves identity.
Card 19 of 20
MediumStudy card 19
Prompt
What content is deliberately outside this topic's scope?
Answer
General trinomial factoring; it belongs to the later quadratic-functions chapter.
Card 20 of 20
HardStudy card 20
Prompt
What is the complete grouping checklist?
Answer
Pair, factor each pair, normalize signs, extract the common binomial, then expand to verify.
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