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

*label*Mathematics

*timer*Asked: Oct 9th, 2016

*account_balance_wallet*$5

### Question Description

Compare and contrast the
different methods for factoring trinomials of the form ax^{2}+
bx + c.

## Tutor Answer

I hope this is sufficient, but ask if you have any questions.

Factoring trinomials

ππ₯ 2 + ππ₯ + π, assume π β 0 (or it isnβt 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 ππ₯ 2 + ππ₯ + π = π(π₯ β π₯1 )(π₯ β π₯2 ).

1.1. Quadratic formula.

1.1.1. The general case.

For the non-negative discriminant π· = π 2 β 4ππ the roots are π₯1 =

βπββπ·

2π

and π₯1 =

βπ+βπ·

.

2π

1.1.2. The case o...

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