Equations

# 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, x_{1} and x_{2}, and then:

ax^{2} + bx + c = a·(x – x_{1})·(x – x_{2})

Examples:

x^{2} – 4x + 4 = (x - 2)^{2}

x^{2} – 5x + 4 = (x – 1)·(x – 4)

**Exercise**: decompose these polynomials:

a) x^{2} + 5x + 6

b) 2x^{2} -3x + 1

c) x^{2} - 12x + 36 = 0

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

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