Lesson 2 of 5
Use sum-product pairs, AC splitting, grouping, and the zero-product rule.
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Worked example
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Factor . Check: 2 and 3 multiply to 6 and add to 5, so the factors are .
Big ideas
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For a trinomial , seek and . Then the factorization is , checked by expansion.
For , the AC method seeks and . Split into , then factor by grouping; take out a GCF first.
In grouping, factor each pair of terms so the remaining binomial matches. A negative GCF may be needed to make both binomials identical.
If a product equals zero, at least one factor is zero. First make one side of an equation zero; factors of an expression alone are not solutions until an equation is specified.
Worked example
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Factor . The AC product is 18 and the split is . Group to get . Expansion restores all three coefficients.
Step-through
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Factor using AC.
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Worked example
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Worked example
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Mix-up alert
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Wrong idea: factors can be set equal to zero when the product equals 12. Repair: the zero-product rule requires zero. Rearrange the equation first, then factor the resulting expression.
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For , what must p and q satisfy?
and .
What product is used in the AC method?
a times c.
What is the sum condition in AC?
.
Factor .
(x-5)().
Factor .
(2x+1)(x+3).
What does AB=0 imply over the reals?
or , or both.
Does every integer-coefficient quadratic factor over integers?
No. State the intended coefficient set.
How do you check grouped factors?
Expand and compare all coefficients.
True or false
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Self-test
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6 questions. One at a time.
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Self-test
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6 questions. One at a time.
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