Decomposition of a polynomial of degree 2

To decompose a polynomial of degree 2 in factors, we have to check if it comes from a remarkable identity, and if it doesn’t, we have to calculate the solutions of the associated equation, x₁ and x₂, and then:
ax² + bx + c = a·(x – x₁)·(x – x₂)

Examples:

x² – 4x + 4 = (x - 2)²

x² – 5x + 4 = (x – 1)·(x – 4)

Exercise: decompose these polynomials:

a) x² + 5x + 6

b) 2x² -3x + 1

c) x² - 12x + 36 = 0

Solutions: a) (x + 2)(x + 3); b) 2(x - 1)(x - 1/2); c) (x - 6)²