Question

Are use factoring to solve the quadratic equation. Check by substitution or by using a graph utility and identifying X interceptsFind the solution set

Answer 1

$S=\lbrace-4,8\rbrace$

1) Let's factor this quadratic equation. Note that we need to find the sum of two numbers whose sum is -4, and the product equal to -32

$\begin{gathered} S=-8+4=-4 \\ P=-8\times4=-32 \end{gathered}$

2) So let's rewrite 4x as the sum of -8 and -4:

$\begin{gathered} x^2-8x+4x-32 \\ x(x-8)+4(x-8) \\ (x+4)(x-8) \end{gathered}$

So let's find the roots equation for each factor above to zero:

$\begin{gathered} (x+4)=0,x=-4 \\ x-8=0,x=8 \\ S=\mleft\lbrace-4,8\mright\rbrace \end{gathered}$