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 minus 8 right parenthesis equals 0

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

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

(x−4)(x−8)=0

Answer 1

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

The numbers $8$ and $-4$ meet these criteria because:

• $8\times (-4)=-32$
• $8+(-4)=4$

Thus, we can factor the quadratic as follows:

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

Therefore, the correct factored form is:

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