Factorise x²+5x+6 in the form of (a+b)²

To factor \(x^2 + 5x + 6\) in the form of \((a+b)^2\), we first need to consider if the expression can be written as a perfect square trinomial. 

A perfect square trinomial takes the form:

\[
(a + b)^2 = a^2 + 2ab + b^2
\]

Looking at \(x^2 + 5x + 6\), it is not directly in this form because it does not match the structure of a perfect square trinomial.

However, we can still factor it in a standard way:

1. The expression is \(x^2 + 5x + 6\).
2. We need two numbers that multiply to give 6 and add up to 5.
   - These numbers are 2 and 3 because \(2 \times 3 = 6\) and \(2 + 3 = 5\).
   
So we factor it as:

\[
x^2 + 5x + 6 = (x + 2)(x + 3)
\]

This is the simplest factorization. Unfortunately, it cannot be written exactly as \((a + b)^2\) because it doesn't form a perfect square trinomial.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you recognize a perfect square trinomial?
2. Can you explain how to complete the square for non-perfect trinomials?
3. How does the discriminant help in determining the factorability of a quadratic?
4. What is the difference between factoring and expanding an algebraic expression?
5. How would you apply this factoring technique to solve a quadratic equation?

**Tip:** A perfect square trinomial always has a middle term that is twice the product of the square roots of the first and last terms.

Factorise x²+5x+6 in the form of (a+b)².

Explore how to factor the quadratic equation x² + 5x + 6 and understand why it cannot be expressed as a perfect square trinomial. Detailed step-by-step guidance for students in Grades 8-10, covering key algebraic concepts such as factoring and quadratic equations.

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