Factor. A) x^2+2x+1 B)x^2+11x+30

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A. we have

x^2+2x+1

we can write it as

x^2+x+x+1

=x(x+1)+1(x+1)

=(x+1)(x+1)

=(x+1)^2

B. We have

x^2+11x+30

factorize 30, we write 30=5 .6

=x^2+(5+6)x+30 (spilit middle term)

=x^2+5x+6x+30

=x(x+5)+6(x+5)

=(x+5)(x+6)

This method is called spiliting middle term method.

`A)` `x^2+2x+1` Factorizating set it equal zero:

`x^2+2x+1=0` `Delta= 4-4(1)=0` ha only a solution as a twice.

`x=(-2+-0)/2` `x_1=x_2=-1`

`x^2+2x+1=(x+1)(x+1)=(x+1)^2`

`B)` `x^2+11x+30`

in order to factiorize it we need to set it equal zero:

`x^2+11x+30=0`

`Delta= 121-4(30)=1` hastwo differetn solutions

`x=(-11+-sqrt(1))/2` `x_1=-5` `x_2=-6```

so: `x^2+11x+30=(x+5)(x+6)`

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