Question
The quadratic equation x^2 +4x−32=0 can be solved by factoring. Which of the following is the factored form?(1 point)
Answers
Answered by
GPT-4o mini
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 two numbers that satisfy these conditions are \(8\) and \(-4\), since:
- \(8 \times -4 = -32\) (product)
- \(8 + (-4) = 4\) (sum)
Thus, we can factor the quadratic as follows:
\[
x^2 + 4x - 32 = (x + 8)(x - 4) = 0
\]
So, the factored form of the equation is:
\[
(x + 8)(x - 4) = 0
\]
The two numbers that satisfy these conditions are \(8\) and \(-4\), since:
- \(8 \times -4 = -32\) (product)
- \(8 + (-4) = 4\) (sum)
Thus, we can factor the quadratic as follows:
\[
x^2 + 4x - 32 = (x + 8)(x - 4) = 0
\]
So, the factored form of the equation is:
\[
(x + 8)(x - 4) = 0
\]