Question
4x^2+20x+25 factored
Answers
Answered by
GPT-4o mini
To factor the quadratic expression \(4x^2 + 20x + 25\), we can look for a perfect square trinomial.
1. First, notice that the expression can be rewritten by factoring out a common factor of \(4\):
\[
4(x^2 + 5x + \frac{25}{4})
\]
2. Next, we can factor the quadratic inside the parentheses. We want to express \(x^2 + 5x + \frac{25}{4}\) in the form \((x + a)^2\).
3. The expression \(x^2 + 5x + \frac{25}{4}\) can be recognized as a perfect square because:
\[
\left(\frac{5}{2}\right)^2 = \frac{25}{4}
\]
4. Thus, we have:
\[
x^2 + 5x + \frac{25}{4} = \left(x + \frac{5}{2}\right)^2
\]
5. Now substituting back into the expression gives:
\[
4\left(x + \frac{5}{2}\right)^2
\]
Therefore, the factored form of \(4x^2 + 20x + 25\) is:
\[
\boxed{4\left(x + \frac{5}{2}\right)^2}
\]
1. First, notice that the expression can be rewritten by factoring out a common factor of \(4\):
\[
4(x^2 + 5x + \frac{25}{4})
\]
2. Next, we can factor the quadratic inside the parentheses. We want to express \(x^2 + 5x + \frac{25}{4}\) in the form \((x + a)^2\).
3. The expression \(x^2 + 5x + \frac{25}{4}\) can be recognized as a perfect square because:
\[
\left(\frac{5}{2}\right)^2 = \frac{25}{4}
\]
4. Thus, we have:
\[
x^2 + 5x + \frac{25}{4} = \left(x + \frac{5}{2}\right)^2
\]
5. Now substituting back into the expression gives:
\[
4\left(x + \frac{5}{2}\right)^2
\]
Therefore, the factored form of \(4x^2 + 20x + 25\) is:
\[
\boxed{4\left(x + \frac{5}{2}\right)^2}
\]