Question

Factorizar 3(a-b)²+5(a-b)+2

Answer 1

$3(a-b)^2+5(a-b) +2\ sustituimos \ (a-b) \ por \ x \\ \\ 3(a-b)^2+5(a-b) +2\to 3x^2+5x+2\ ahora \ aplicamos \ Bascara \\ \\ x_ {1\ y\ 2}= \frac{-b\pm \sqrt{b^2-4ac}}{2a} \qquad a=3\quad b=5\quad c=2 \\ \\ x_ {1\ y\ 2}= \frac{-5\pm \sqrt{25-4(3)(2)}}{2.3} \\ \\ x_ {1\ y\ 2}= \frac{-5\pm \sqrt{25-24}}{6} \to x_ {1\ y\ 2}= \frac{-5\pm \sqrt{1}}{6} \to x_ {1\ y\ 2}= \frac{-5\pm 1}{6} \\ \\ x_1= \frac{-5+1}{6}\to x_1= \frac{-4}{6}\to x_1= - \frac{2}{3}$

$x_2= \frac{-5-1}{6}\to x_2= \frac{-6}{6}\to x_2= -1$



$Entonces \qquad 3x^2+5x+2 = (x +\frac{2}{3})(x+1) \to Factorizado \\ \\ Reemplazamos \ (a-b) =x \\ \\ 3(a-b)^2+5(a-b) +2 = \left[(a-b)+ \frac{2}{3} \right] \left[(a-b)+1}\right] \to Factorizado \ \checkmark$


Espero que te sirva, salu2!!!!