Explain how to factor the following trinomials forms: x2 + bx + c and ax2 + bx + c. Is there more than one way to factor this? Show your answer using both words and mathematical notation.
Let's factor the trinomial x² + bx + c. We know that if b²-4c >= 0 then this trinomial has zeros and it can be factorized. It's zeros are
x1 = [ -b + √(b²-4c) ] / 2
x2 = [ -b - √(b²-4c) ] / 2.
So, we can factor it as
x² + bx + c = (x-x1)(x-x2).
In a case of trinomial ax² + bx + c we can factorize it as
ax² + bx + c = a(x² + b/a·x + c/a),
where the trinomial x² + b/a·x + c/a has the same form as x² + bx + c.