(x+2)^2-(x+2)-42

Question

Factor this equation please someone?

Answer 1

( a + b ) ^ 2 = a ^ 2 + 2 a b + b ^ 2

so:

( x + 2 ) ^ 2 = x ^ 2 + 2 x * 2 + 2 ^ 2 = x ^ 2 + 4 x + 4

( x + 2 ) ^ 2 - ( x + 2 ) - 42 =

x ^ 2 + 4 x + 4 - x - 2 - 42 =

x ^ 2 + 4 x + 4 - x - 44 =

x ^ 2 + 4 x - x + 4 - 44 =

x ^ 2 + 3 x - 40

Find two numbers whose product is - 40 and whose sum is 3.

The numbers are: - 8 an 5 becouse:

( - 8 ) * 5 = - 40

and - 8 + 5 = 3

So:

x ^ 2 + 3 x - 40 = [ x - ( - 8 ) ] ( x - 5 ) = ( x + 8 ) ( x - 5 )

Answer 2

The numbers are: 8 an - 5 becouse:

8 * ( - 5 ) = - 40

and 8 - 5 = 3

x ^ 2 + 3 x - 40 = ( x + 8 ) ( x - 5 )

Answer 3

(x+2)^2-(x+2)-42
Note that (u-7)(u+6) = u^2-u-42

So, letting u=x+2, we have

(x+2-7)(x+2+6) = 0
(x-5)(x+8) = 0
as above

Answer 4

tres bien