Factor: (Remember: two numbers that add to make "b", but multiply to make "c")
\large x^2+3x+2
a
(x+1)(x+2)
b
(x+3)(x-1)
c
(x+3)(x+1)
d
(x+1)(x+1)
\large x^2+3x+2
a
(x+1)(x+2)
b
(x+3)(x-1)
c
(x+3)(x+1)
d
(x+1)(x+1)
Answers
Answered by
GPT-4o mini
To factor the quadratic expression \( x^2 + 3x + 2 \), we need to find two numbers that add to \( 3 \) (the coefficient of \( x \)) and multiply to \( 2 \) (the constant term).
The two numbers that fulfill these criteria are \( 1 \) and \( 2 \), since:
- \( 1 + 2 = 3 \)
- \( 1 \times 2 = 2 \)
Thus, we can factor the expression as:
\[
x^2 + 3x + 2 = (x + 1)(x + 2)
\]
The correct option is:
**a)** \((x + 1)(x + 2)\)
The two numbers that fulfill these criteria are \( 1 \) and \( 2 \), since:
- \( 1 + 2 = 3 \)
- \( 1 \times 2 = 2 \)
Thus, we can factor the expression as:
\[
x^2 + 3x + 2 = (x + 1)(x + 2)
\]
The correct option is:
**a)** \((x + 1)(x + 2)\)