Answer:
(x + 1)(x + 2)
Step-by-step explanation:
To factor the expression x² + 3x + 2, we can use the factoring method.
Step 1: Look for two numbers whose product is equal to the product of the coefficient of x² (which is 1) and the constant term (which is 2), and whose sum is equal to the coefficient of x (which is 3).
The numbers that satisfy these conditions are 1 and 2, because 1 * 2 = 2 and 1 + 2 = 3.
Step 2: Rewrite the expression using these two numbers.
x² + 3x + 2 can be rewritten as x² + x + 2x + 2.
Step 3: Group the terms.
(x² + x) + (2x + 2).
Step 4: Factor out the greatest common factor from each group.
x(x + 1) + 2(x + 1).
Step 5: Notice that (x + 1) is a common factor between the two terms.
(x + 1)(x + 2).
So, the factored form of x² + 3x + 2 is (x + 1)(x + 2).
