Question
x^2 + 5x - 14 factorization (x-2)(x+7)
Answers
GPT-4o mini
To factor the quadratic expression \( x^2 + 5x - 14 \), we want to find two numbers that multiply to \(-14\) (the constant term) and add to \(5\) (the coefficient of \(x\)).
Let's look at the factors of \(-14\):
- \(1\) and \(-14\) (sum is \(-13\))
- \(-1\) and \(14\) (sum is \(13\))
- \(2\) and \(-7\) (sum is \(-5\))
- \(-2\) and \(7\) (sum is \(5\))
The correct pair that adds up to \(5\) is \(-2\) and \(7\).
Thus, we can rewrite the expression:
\[
x^2 + 5x - 14 = (x - 2)(x + 7)
\]
So, the factorization of \(x^2 + 5x - 14\) is \((x - 2)(x + 7)\). Your factorization is correct!
Let's look at the factors of \(-14\):
- \(1\) and \(-14\) (sum is \(-13\))
- \(-1\) and \(14\) (sum is \(13\))
- \(2\) and \(-7\) (sum is \(-5\))
- \(-2\) and \(7\) (sum is \(5\))
The correct pair that adds up to \(5\) is \(-2\) and \(7\).
Thus, we can rewrite the expression:
\[
x^2 + 5x - 14 = (x - 2)(x + 7)
\]
So, the factorization of \(x^2 + 5x - 14\) is \((x - 2)(x + 7)\). Your factorization is correct!