Practice and apply :Factor each trinomial if it is not factorable .write prime ×²+8×+16

To factor the trinomial \( x^2 + 8x + 16 \), let's follow these steps:

### Step 1: Identify the coefficients
The trinomial is of the form \( ax^2 + bx + c \), where:
- \( a = 1 \) (coefficient of \( x^2 \))
- \( b = 8 \) (coefficient of \( x \))
- \( c = 16 \) (constant term)

### Step 2: Check if the trinomial is a perfect square
A trinomial is a perfect square if it can be written as \( (mx + n)^2 \).

Check if:
1. \( m^2 = a \) (in this case, \( m = 1 \))
2. \( 2mn = b \) (this means \( 2(1)(n) = 8 \))
3. \( n^2 = c \) (this means \( n^2 = 16 \))

From \( 2mn = 8 \), solving for \( n \):
\[ n = \frac{8}{2 \times 1} = 4 \]

Now, check if \( n^2 = c \):
\[ 4^2 = 16 \]

This confirms that the trinomial is a perfect square.

### Step 3: Write the factorization
So, \( x^2 + 8x + 16 \) factors as:
\[ (x + 4)^2 \]

### Final Answer:
The factorization of the trinomial \( x^2 + 8x + 16 \) is:
\[ (x + 4)(x + 4) \]
or simply \( (x + 4)^2 \).

This trinomial is factorable and is not prime.

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Would you like more details or have any questions?

Here are 5 relative questions you can practice with:

1. Factor the trinomial: \( x^2 + 6x + 9 \).
2. Determine if the trinomial \( x^2 + 7x + 10 \) is factorable.
3. Factor the expression \( x^2 + 10x + 25 \).
4. Factor the quadratic expression \( x^2 + 4x + 4 \).
5. Is the trinomial \( x^2 + 9x + 20 \) a perfect square?

**Tip:** Always check if a trinomial is a perfect square before factoring. This can save you time!

Learn how to factor the trinomial x^2 + 8x + 16 with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring perfect square trinomials and quadratic equations. Suitable for students in Grades 7-9.

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