Question
Factor completely. If the polynomial is prime, state so. \( x^{2}+12 x+36 \)
Ask by Gibbs Hall. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
(x + 6)^2
\]
Solution
The given polynomial is:
\[
x^2 + 12x + 36
\]
To factor this quadratic, we look for two numbers that multiply to \( 36 \) (the constant term) and add up to \( 12 \) (the coefficient of the middle term).
These numbers are \( 6 \) and \( 6 \), since:
\[
6 \times 6 = 36 \quad \text{and} \quad 6 + 6 = 12
\]
Thus, the polynomial can be written as:
\[
(x + 6)(x + 6) = (x + 6)^2
\]
**Final Answer:**
\[
(x + 6)^2
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
The expression \( x^{2}+12x+36 \) can be factored as \( (x+6)(x+6) \) or \( (x+6)^2 \). This shows that it is a perfect square trinomial. Because we were able to factor it into a product of binomials, this polynomial is not prime; it has factors that can be expressed more simply.
