The quadratic equation x2+4x−32=0

Question

𝑥
2
+
4
𝑥
−
32
=
0
can be solved by factoring. Which of the following is the factored form?(1 point)
Responses

(x+8)(x−4)=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
(
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
(
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

Answer 1

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

The pairs of factors of \(-32\) are:

• \(1\) and \(-32\)
• \(-1\) and \(32\)
• \(2\) and \(-16\)
• \(-2\) and \(16\)
• \(4\) and \(-8\)
• \(-4\) and \(8\)

Among these pairs, the pair \(8\) and \(-4\) adds up to \(4\).

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

So, the factored form of the quadratic equation \(x^2 + 4x - 32 = 0\) is: \[ (x + 8)(x - 4) = 0 \]

Therefore, the correct response is: \[ (x + 8)(x - 4) = 0 \]