Question

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.

Answer 1

\[x=[-b \pm \sqrt{b ^{2}-4ac}]\div2a\]

Answer 2

ax2 + bx + c
a(x2+bx/a+c/a)
a(x2+2(b/2a)x+c/a)
a(x2+2(b/2a)x+(b/2a)^2-(b/2a)^2+c/a)
a[(x+b/2a)^2+(-b^2+4ac)/4a^2
a[(x+b/2a)^2-(b^2-4ac)/4a^2
a[(x+b/2a)^2-\[[\sqrt{b^2-4ac}/2a]^2\]
{a[x+b/2a]}+rt(b^2-4ac)/2a}{a[x+b/2a]}-rt(b^2-4ac)/2a}