Description
Compare and contrast the different methods for factoring trinomials of the form ax2+ bx + c.
Explanation & Answer
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Factoring trinomials
𝑎𝑥 2 + 𝑏𝑥 + 𝑐, assume 𝑎 ≠ 0 (or it isn’t a trinomial).
The common: all these methods give the same result. The differences are in the process.
1. Finding the roots.
If the trinomial has no real roots, it cannot be factored (in real numbers; complex roots exist always).
If it has the roots 𝑥1 and 𝑥2 (they may coincide), then 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 𝑎(𝑥 − 𝑥1 )(𝑥 − 𝑥2 ).
1.1. Quadratic formula.
1.1.1. The general case.
For the non-negative discriminant 𝐷 = 𝑏 2 − 4𝑎𝑐 the roots are 𝑥1 =
−𝑏−√𝐷
2𝑎
and 𝑥1 =
−𝑏+√𝐷
.
2𝑎
1.1.2. The case o...
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