Question

Buenas noches.
Como se factoriza
9t² - 12t -4

2t² - 7t + 6

3q² + 20q + 32

Answer 1

$Todos \ se \ factorizan \ aplicando \ bascara \\ \\ \frac{-b\pm \sqrt{b^2-4ac}}{2a}, entonces \\ \\ a) \ 9t^2-12t-4 \\ \\ \frac{12\pm \sqrt{144-4(9)(-4)}}{2*9}\to \frac{12\pm \sqrt{144-144}}{18}\to \frac{12\pm \sqrt{0}}{18} \\ \\ t_1=t_2= \frac{2}{3} \\ \\ b) \ 2t^2-7t+6 \\ \\ \frac{7\pm \sqrt{49-4(2)(6)}}{2*2}\to \frac{7\pm \sqrt{49-48}}{4}\to \frac{7\pm \sqrt{1}}{4} \to\frac{7\pm 1}{4} \\ \\ t_1= \frac{8}{4}\to t_1=2\qquad\quad t_2= \frac{6}{4}\to t_2= \frac{3}{2}$

$c) 3q^2+20q+32 \\ \\ \frac{-20\pm \sqrt{400-4(3)(32)}}{2*3}\to \frac{-20\pm \sqrt{400-384}}{6}\to \frac{-20\pm \sqrt{16}}{6} \to\frac{-20\pm 4}{6} \\ \\ t_1= \frac{-16}{6}\to t_1=- \frac{8}{3} \qquad\quad t_2= \frac{-24}{6}\to t_2= -4$

Espero que te sirva, salu2!!!!