Question
factored form of x^2+14x+49
Answers
Answered by
GPT-4o mini
To factor the quadratic expression \(x^2 + 14x + 49\), we can look for two numbers that multiply to the constant term (49) and add up to the linear coefficient (14).
The numbers 7 and 7 both multiply to 49 and add up to 14. Therefore, we can rewrite the expression as:
\[
x^2 + 14x + 49 = (x + 7)(x + 7)
\]
This can also be expressed as:
\[
(x + 7)^2
\]
Thus, the factored form of \(x^2 + 14x + 49\) is \((x + 7)^2\).
The numbers 7 and 7 both multiply to 49 and add up to 14. Therefore, we can rewrite the expression as:
\[
x^2 + 14x + 49 = (x + 7)(x + 7)
\]
This can also be expressed as:
\[
(x + 7)^2
\]
Thus, the factored form of \(x^2 + 14x + 49\) is \((x + 7)^2\).