Question
Factor.
x, squared, plus, 3, x, plus, 2
x
2
+3x+2
x, squared, plus, 3, x, plus, 2
x
2
+3x+2
Answers
GPT-4o mini
To factor the quadratic expression \( x^2 + 3x + 2 \), we need to find two numbers that multiply to \( 2 \) (the constant term) and add to \( 3 \) (the coefficient of the linear term).
The numbers \( 1 \) and \( 2 \) meet these requirements since:
- \( 1 \times 2 = 2 \)
- \( 1 + 2 = 3 \)
Therefore, we can factor the expression as:
\[
x^2 + 3x + 2 = (x + 1)(x + 2)
\]
Thus, the factored form of \( x^2 + 3x + 2 \) is \( (x + 1)(x + 2) \).
The numbers \( 1 \) and \( 2 \) meet these requirements since:
- \( 1 \times 2 = 2 \)
- \( 1 + 2 = 3 \)
Therefore, we can factor the expression as:
\[
x^2 + 3x + 2 = (x + 1)(x + 2)
\]
Thus, the factored form of \( x^2 + 3x + 2 \) is \( (x + 1)(x + 2) \).