Question

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

Answer 1

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)"✔"`