A Brief Review of Factoring
Ex:
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Form: 𝑥 2 + 𝑏𝑥 + 𝑐
(Notice that the leading coefficient is 1)
Steps:
1. Find integers that multiply to be 𝑐.
2. Of those, choose the pair that adds to be 𝑏.
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If no such integers exist, then it’s prime.
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Ex:
𝑣 2 − 5𝑣𝑦 − 14𝑦 2 = (𝑣 − 7𝑦)(𝑣 + 2𝑦)
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Form: 𝑎𝑥 2 + 𝑏𝑥 + 𝑐, 𝑎 ≠ 1
(Notice that the leading coefficient is not 1)
Use the 𝑎𝑐 method: (𝑎𝑐 = −24 below)
Solving Equations by Factoring
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Heavily relies on the Zero-Factor Property.
5 ∙ ?= 0
? ∙ 12 = 0
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Hence, given an equation we will . . .
1) Get zero on one side.
2) Factor the equation.
3) Set each of the factors equal to zero.
4) Solve.
Solve.
Solve.
Solve.
Solve.
Solve.
Solve.
Solve.
Solve.
Solve.
Solve.
Solve.
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