How do you factor #x^2 + 4x + 3#?

1 Answer
Proteus
Jun 1, 2016

It is #(x+1)(x+3)#

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1. Break the expression into groups

#color(blue)"How?"#
- For formula #ax^2+bx+c# find #u#, #v# such that #u·v=a· c# and #u+v=b#
Now just group according to this: #(ax^2+ux)+(vx+c)#

#color(green)"Insert numbers:"#

#=># #(x^2+x)+(3x+3)r#

2. Factor out
#color(orange)"-"# Factor out #x# from #x^2+x# #=># #x(x+1)#
#color(lightblue)"-"# Factor out #3# from #3x+3# #=># #3(x+1)#
#=x(x+1)+3(x+1)#

  1. Factor out the common term which is #(x+1)#

#=(x+1)(x+3)

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Done #color(darkgreen)"✔"#

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