Question
How would you Factor the expression *
X^2-X-42
X^2-X-42
Answers
GPT-4o mini
To factor the quadratic expression \( X^2 - X - 42 \), we will look for two numbers that multiply to \(-42\) (the constant term) and add up to \(-1\) (the coefficient of the linear term).
The two numbers that satisfy these conditions are \( 6 \) and \(-7\) because:
- \( 6 \times (-7) = -42 \)
- \( 6 + (-7) = -1 \)
Thus, we can express the quadratic as:
\[
X^2 - X - 42 = (X + 6)(X - 7)
\]
Therefore, the factored form of \( X^2 - X - 42 \) is:
\[
(X + 6)(X - 7)
\]
The two numbers that satisfy these conditions are \( 6 \) and \(-7\) because:
- \( 6 \times (-7) = -42 \)
- \( 6 + (-7) = -1 \)
Thus, we can express the quadratic as:
\[
X^2 - X - 42 = (X + 6)(X - 7)
\]
Therefore, the factored form of \( X^2 - X - 42 \) is:
\[
(X + 6)(X - 7)
\]