How do I factor out:

21 - 4x - x^2



x^2 + 4x - 21 = 0
this is of the form (ax + c)(bx + d) = abx^2 + (c+d)x + cd
here ab = 1 so
c+d = 4
cd = -21
therefore c = 7 and d = -3
(x + 7)(x-3)=0
x = -7 and x = 3

To factor the expression 21 - 4x - x^2, we can rewrite it in the form of a quadratic equation: x^2 + 4x - 21 = 0.

To factor a quadratic equation, we need to find two numbers that, when multiplied together, give us the coefficient of the squared term (a = 1) multiplied by the constant term (c = -21), and when added together, give us the coefficient of the linear term (b = 4).

In this case, we need to find two numbers whose product is -21 and whose sum is 4. The two numbers that satisfy these conditions are 7 and -3.

So, we can rewrite the quadratic equation as (x + 7)(x - 3) = 0.

By using the zero product property, we know that the equation is equal to zero when either (x + 7) = 0 or (x - 3) = 0.

Therefore, by solving each equation separately, we find that x = -7 and x = 3 are the solutions to the quadratic equation x^2 + 4x - 21 = 0, which is equivalent to factoring out 21 - 4x - x^2.