Compare and contrast the different methods for factoring trinomials of the form

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Compare and contrast the different methods for factoring trinomials of the form ax2+ bx + c.


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Borys_S
School: UIUC

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Factoring trinomials
π‘Žπ‘₯ 2 + 𝑏π‘₯ + 𝑐, assume π‘Ž β‰  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 π‘₯1 and π‘₯2 (they may coincide), then π‘Žπ‘₯ 2 + 𝑏π‘₯ + 𝑐 = π‘Ž(π‘₯ βˆ’ π‘₯1 )(π‘₯ βˆ’ π‘₯2 ).
1.1. Quadratic formula.
1.1.1. The general case.
For the non-negative discriminant 𝐷 = 𝑏 2 βˆ’ 4π‘Žπ‘ the roots are π‘₯1 =

βˆ’π‘βˆ’βˆšπ·
2π‘Ž

and π‘₯1 =

βˆ’π‘+√𝐷
.
2π‘Ž

1.1.2. The case o...

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