Question

The Solving Quadratic Equations Using Patterns Quick Check

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

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 the linear term).

The two numbers that meet these criteria are \(8\) and \(-4\) because:

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

Thus, we can express the quadratic equation in factored form as:

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

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

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