The quadratic equation x2+4x−32=0 can be solved by factoring. Which of the following is the factored form?

Question

A) (x + 4) (x - 8) = 0
B) (x + 8) (x - 4) = 0
C) (x - 4) (x - 8) = 0
D) (x + 4) (x + 8) = 0

Answer 1

To factor the quadratic equation \( x^2 + 4x - 32 = 0 \), we need to find two numbers that multiply to \(-32\) (the constant term) and add up to \(4\) (the coefficient of \(x\)).

The numbers \(8\) and \(-4\) fit these requirements:

• \(8 \times -4 = -32\)
• \(8 + (-4) = 4\)

Thus, we can factor the equation as: \[ (x + 8)(x - 4) = 0 \]

So the correct answer is: B) (x + 8) (x - 4) = 0.