Answer:
[tex]\fbox{\begin{minipage}{6em}(f +4)(f - 5)\end{minipage}}[/tex]
Explanation:
Step 1: Add more suitable components
[tex]A = f^{2} - f - 20[/tex]
[tex]A = f^{2} + 4f - 5f - 20[/tex]
Step 2: apply associative property
[tex]A = f(f + 4) - 5(f + 4)[/tex]
Step 3: combine the common components
[tex]A = (f + 4)(f - 5)[/tex]
Note:
To factorize an expression in form of [tex]f^{2} + bf + c[/tex], the coefficient [tex]b[/tex] is often turned into the sum of 2 new components [tex]b_{1}[/tex] and [tex]b_{2}[/tex] that satisfy [tex]b_{1}[/tex] x [tex]b_{2}[/tex] = [tex]c[/tex]
In the above problem: [tex]b[/tex] = -1, is then turned into [tex]b_{1} = 4[/tex] and [tex]b_{2} = -5[/tex], that satisfy [tex]b_{1}[/tex] x [tex]b_{2}[/tex] = [tex](4)[/tex] x [tex](-5)[/tex] = [tex]-20[/tex] = [tex]c[/tex]
Hope this helps!
:)
