Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
(x + 4)^2
\]
Solution
To factor the quadratic polynomial \( x^{2} + 8x + 16 \), follow these steps:
1. **Identify the coefficients**:
- \( a = 1 \) (coefficient of \( x^2 \))
- \( b = 8 \) (coefficient of \( x \))
- \( c = 16 \) (constant term)
2. **Find two numbers that multiply to \( c \) (16) and add up to \( b \) (8)**:
- The numbers are **4 and 4** because:
\[
4 \times 4 = 16 \quad \text{and} \quad 4 + 4 = 8
\]
3. **Write the factored form using these numbers**:
\[
x^{2} + 8x + 16 = (x + 4)(x + 4)
\]
- This can also be written as:
\[
(x + 4)^2
\]
**Final Answer**:
\[
(x + 4)^2
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
Sure thing! Here’s a fun breakdown of the factorization: This polynomial, \( x^{2}+8x+16 \), is a perfect square. You may notice that the coefficients nicely fit into the form \( (a + b)^2 = a^2 + 2ab + b^2 \). In this case, you can rewrite it as \( (x + 4)^2 \), since \( 4^2 = 16 \) and \( 2 \cdot 4 \cdot x = 8x \). So the factored form is: \[ (x + 4)(x + 4) \] or simply \( (x + 4)^2 \). Now you have a neat and tidy way to express this polynomial!
