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

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user2324818 | (Level 2) eNoter

Posted April 27, 2013 at 11:48 AM via iOS

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

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted April 27, 2013 at 12:05 PM (Answer #1)

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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.

 

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oldnick | (Level 1) Valedictorian

Posted April 28, 2013 at 12:29 AM (Answer #2)

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`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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