Question

Factor this trinomial into a product of binomial factors.
x² − 12x − 35 = [

Answer 1

`~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-12}x\stackrel{\stackrel{c}{\downarrow }}{-35}=y \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x= \cfrac{ - (-12) \pm \sqrt { (-12)^2 -4(1)(-35)}}{2(1)} \implies x = \cfrac{ 12 \pm \sqrt { 144 +140}}{ 2 } \\\\\\ x= \cfrac{ 12 \pm \sqrt { 284 }}{ 2 }\implies x= \cfrac{ 12 \pm 2\sqrt { 71 }}{ 2 }\implies x=6\pm√(71) \\\\[-0.35em] ~\dotfill`

`x=6+√(71)\implies x-6-√(71)=0 \\\\[-0.35em] ~\dotfill\\\\ x=6-√(71)\implies x-6+√(71)=0 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} (x-6-√(71))(x-6+√(71)) \end{array}}~\hfill`