Respuesta :
[tex]\text{Given: }7-48x-7x^2[/tex]
Since the given trinomial is a quadratic expression. We can factor this using a quadratic formula.
[tex]x=\frac{ -b \pm\sqrt{b^2 - 4ac}}{ 2a }[/tex][tex]\begin{gathered} \text{Rearrange the expression so that it is in the form }ax^2+bx+c \\ \\ 7-48x-7x^2\Rightarrow-7x^2-48x+7 \\ \\ \text{Here, we can determine }a,b,\text{ and }c \\ a=-7 \\ b=-48 \\ c=7 \end{gathered}[/tex]Substitute the following coefficients the quadratic formula and we get:
[tex]\begin{gathered} x=\frac{ -b \pm\sqrt{b^2 - 4ac}}{ 2a } \\ x=\frac{ -(-48) \pm\sqrt{(-48)^2 - 4(-7)(7)}}{ 2(-7) } \\ x=\frac{48\pm\sqrt[]{2304-(-196)}}{-14} \\ x=\frac{ 48 \pm\sqrt{2500}}{ -14 } \\ x=\frac{ 48 \pm50\, }{ -14 } \\ x=-\frac{ 98 }{ 14 }\; \; \; x=\frac{ 2 }{ 14 } \\ x=-7\; \; \; x=\frac{ 1}{ 7 } \end{gathered}[/tex]Equate the solution to zero to get the factors.
[tex]\begin{gathered} x=-7 \\ x+7=0 \\ \\ x=\frac{1}{7} \\ x-\frac{1}{7}=0 \\ 7x-1=0 \\ \\ \text{Therefore, the factor of }7-48x-7x^2\text{ is }(x+7)(7x-1) \end{gathered}[/tex]