Question

Представьте в виде произведения двух линейных множителей с целыми коэффициентами.
6z^2+25z+14
-12m^2-11m+15
8k^2-27k-20

Answer 1

$1)6z^{2}+25z+14=0\\\\D=25^{2}-4*6*14=625-336=289=17^{2}\\\\z_{1}=\frac{-25-17}{12}=-\frac{42}{12}=-\frac{7}{2}\\\\z_{2}=\frac{-25+17}{12}=-\frac{8}{12}=-\frac{2}{3}\\\\6z^{2}+25z+14=6(z+\frac{7}{2})(z+\frac{2}{3})=(2z+7)(3z+2)$

$2)-12m^{2}-11m+15=0\\\\12m^{2}+11m-15=0\\\\D=11^{2}-4*12*(-15)=121+720=841=29^{2}\\\\m_{1}=\frac{-11-29}{24} =-\frac{5}{3}\\\\m_{2}=\frac{-11+29}{24}=\frac{3}{4} \\\\-12m^{2}-11m+15=-12(m+\frac{5}{3})(m-\frac{3}{4})=(3m+5)(3-4m)$

$3)8k^{2}-27k-20=0\\\\D=(-27)^{2}-4*8*(-20)=729+640=1369=37^{2}\\\\k_{1}=\frac{27-37}{16}=-\frac{5}{8}\\\\k_{2}=\frac{27+37}{16}=4\\\\8k^{2}-27k-20=8(k+\frac{5}{8})(k-4)=(8k+5)(k-4)$