Question
The quadratic equation x ^ 2 + 4x - 32 = 0 can be solved by factoringWhich of the following is the factored form ? (1 point ) (x + 4)(x - 8) = 0; (x + 8)(x - 4) = 0; (x - 4)(x - 8) = 0; (x + 4)(x + 8) = 0
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Answered by
GPT-4o mini
To factor the quadratic equation \( x^2 + 4x - 32 = 0 \), we are looking for two numbers that multiply to \(-32\) (the constant term) and add to \(4\) (the coefficient of \(x\)).
The numbers that meet these criteria are \(8\) and \(-4\) because:
- \(8 \times (-4) = -32\)
- \(8 + (-4) = 4\)
Using these numbers, we can factor the quadratic as follows:
\[
x^2 + 4x - 32 = (x + 8)(x - 4) = 0
\]
Thus, the correct factored form is:
\((x + 8)(x - 4) = 0\)
So the answer is \((x + 8)(x - 4) = 0\).
The numbers that meet these criteria are \(8\) and \(-4\) because:
- \(8 \times (-4) = -32\)
- \(8 + (-4) = 4\)
Using these numbers, we can factor the quadratic as follows:
\[
x^2 + 4x - 32 = (x + 8)(x - 4) = 0
\]
Thus, the correct factored form is:
\((x + 8)(x - 4) = 0\)
So the answer is \((x + 8)(x - 4) = 0\).
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