The quadratic equation x2+4x−32=0 can be solved by factoring. Which of the following is the factored form?(1 point)

Question

Responses

(x+4)(x+8)=0
left parenthesis x plus 4 right parenthesis left parenthesis x plus 8 right parenthesis equals 0

(x−4)(x−8)=0
left parenthesis x minus 4 right parenthesis left parenthesis x minus 8 right parenthesis equals 0

(x+4)(x−8)=0
left parenthesis x plus 4 right parenthesis left parenthesis x minus 8 right parenthesis equals 0

(x+8)(x−4)=0

Answer 1

To solve the quadratic equation \( x^2 + 4x - 32 = 0 \) by factoring, we want to find two numbers that multiply to \(-32\) (the constant term) and add to \(4\) (the coefficient of the linear term).

The numbers that satisfy these conditions are \(8\) and \(-4\), since:

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

Thus, we can factor the quadratic equation as:

\[ (x + 8)(x - 4) = 0 \]

So, the correct factored form is:

\[ (x + 8)(x - 4) = 0 \]

This corresponds to the response:

(x + 8)(x - 4) = 0.