Question

1. d²+11d+28=02. e²-2e-24=03. 49f²-36=04. g²+15g=0

Answer 1

`\begin{gathered} 1)d^2+11d+28=0 \\ we\text{ search for 2 factors that when added up gives you 11d and when multiplied gives 28 } \\ \text{Those factors are 4d and 7d}\ldots\text{ 4d+7d= 11d}\ldots.\text{ 4d}*7d=\ldots.28d^2 \\ We\text{ now replace 11d by 4d and 7d} \\ so\text{ we have} \\ d^2+4d+7d+28=0 \\ we\text{ now factorize} \\ (d^2+4d)(+7d+28)=0 \\ d(d+4)+7(d+4)=0 \\ (d+4)(d+7)=0 \\ d+4\text{ = 0} \\ d=-4 \\ or \\ d+7\text{ =0} \\ d=-7 \end{gathered}`
`\begin{gathered} 2)e^2-2e-24=0 \\ \text{again we search for two factors that when added gives you -2e and when multiplied gives -24} \\ \text{Those factors are -6e and +4e} \\ -6e\text{ +4e=-2e} \\ -6e\text{ }*4e=-24e^2 \\ We\text{ now replace -2e with the factors} \\ e^2-6e+4e-24=0 \\ \text{We now factorize the equation} \\ (e^2-6e)(+4e-24)=0 \\ e(e-6)+4(e-6)=0 \\ (e-6)(e+4)=0 \\ e-6=\text{ 0} \\ e=6 \\ or \\ e+4=0 \\ e=-4 \end{gathered}`
`\begin{gathered} 4)g^2+15g=0 \\ we\text{ factorize immediately here} \\ g(g+15)=0 \\ g=\text{ 0 or} \\ (g+15)=0 \\ g=-15 \end{gathered}`