Factor the expression x² + 10x + 25.

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Question: Factor the expression x² + 10x + 25.

Options:

Correct Answer: (x + 5)²

Solution:

x² + 10x + 25 = (x + 5)², a perfect square trinomial.

Factor the expression x² + 10x + 25.

Factor the expression x² + 10x + 25.

Step 1: Identify the expression you want to factor, which is x² + 10x + 25.
Step 2: Look for two numbers that multiply to the last term (25) and add up to the middle term (10).
Step 3: The numbers that work are 5 and 5 because 5 * 5 = 25 and 5 + 5 = 10.
Step 4: Rewrite the expression using these numbers: x² + 5x + 5x + 25.
Step 5: Group the terms: (x² + 5x) + (5x + 25).
Step 6: Factor out the common terms in each group: x(x + 5) + 5(x + 5).
Step 7: Now you have a common factor of (x + 5): (x + 5)(x + 5).
Step 8: This can be written as (x + 5)², which is the factored form.

Factoring Quadratic Expressions – The process of rewriting a quadratic expression as a product of its factors.
Perfect Square Trinomials – Recognizing and factoring expressions of the form a² + 2ab + b² as (a + b)².