(x+2)^2-(x+2)-42
Factor this equation please someone?
( 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 )
The numbers are: 8 an - 5 becouse:
8 * ( - 5 ) = - 40
and 8 - 5 = 3
x ^ 2 + 3 x - 40 = ( x + 8 ) ( x - 5 )
(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
tres bien
To factor the equation (x+2)^2 - (x+2) - 42, we can start by simplifying it.
First, let's distribute the exponent of 2 to the terms inside the brackets:
(x+2)(x+2) - (x+2) - 42
Expanding the brackets, we get:
(x^2 + 4x + 4) - (x + 2) - 42
Now, we can combine like terms:
x^2 + 4x + 4 - x - 2 - 42
This simplifies to:
x^2 + 3x - 40
To factor this quadratic equation, we need to find two numbers that multiply to give us -40 and add up to 3. In this case, those numbers are 8 and -5.
So, we can rewrite the equation as:
(x + 8)(x - 5)
The factored form of the equation (x+2)^2 - (x+2) - 42 is (x + 8)(x - 5).