Factor the expression x² + 5x + 6.

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Question: Factor the expression x² + 5x + 6.

Options:

Correct Answer: (x + 2)(x + 3)

Solution:

x² + 5x + 6 = (x + 2)(x + 3) because 2 and 3 add to 5 and multiply to 6.

Factor the expression x² + 5x + 6.

Factor the expression x² + 5x + 6.

Step 1: Identify the expression you want to factor, which is x² + 5x + 6.
Step 2: Look for two numbers that add up to the coefficient of x (which is 5) and multiply to the constant term (which is 6).
Step 3: The two numbers that work are 2 and 3 because 2 + 3 = 5 and 2 * 3 = 6.
Step 4: Rewrite the expression using these two numbers: x² + 2x + 3x + 6.
Step 5: Group the terms: (x² + 2x) + (3x + 6).
Step 6: Factor out the common factors in each group: x(x + 2) + 3(x + 2).
Step 7: Now, you can factor out the common binomial (x + 2): (x + 2)(x + 3).

Factoring Quadratic Expressions – This involves rewriting a quadratic expression in the form ax² + bx + c as a product of two binomials.