Question

question
factor.
$x^2 + 14x + 45$

Explanation:

Step1: Find two numbers that multiply to 45 and add to 14.

We need two numbers \( m \) and \( n \) such that \( m \times n = 45 \) and \( m + n = 14 \). The numbers 5 and 9 work because \( 5 \times 9 = 45 \) and \( 5 + 9 = 14 \).

Step2: Rewrite the middle term using these numbers.

\( x^{2}+5x + 9x+45 \)

Step3: Group the terms and factor by grouping.

Group the first two terms and the last two terms: \( (x^{2}+5x)+(9x + 45) \)
Factor out the greatest common factor from each group: \( x(x + 5)+9(x + 5) \)
Now, factor out the common binomial factor \( (x + 5) \): \( (x + 5)(x + 9) \)

Answer:

\( (x + 5)(x + 9) \)