Question

if $x + 4$ is a factor of $x^2 + 11x + 28$, what is the other factor?\
\bigcirc $x + 12$\
\bigcirc $x + 7$\
\bigcirc $x - 4$\
\bigcirc $x - 7$

Explanation:

Step1: Recall factoring quadratic

We need to factor \(x^2 + 11x + 28\) where one factor is \(x + 4\). For a quadratic \(x^2+bx + c\), we find two numbers that multiply to \(c\) and add to \(b\). Here, \(c = 28\) and \(b = 11\), and one factor's constant term is \(4\), so the other constant term should satisfy \(4\times n=28\) and \(4 + n=11\). Solving \(4\times n = 28\), we get \(n = 7\). So the other factor is \(x + 7\).
Alternatively, we can perform polynomial division or use the fact that \((x + 4)(x + n)=x^2+(4 + n)x+4n\). Comparing with \(x^2 + 11x + 28\), we have \(4 + n=11\) (so \(n = 7\)) and \(4n=28\) (which also gives \(n = 7\)).

Answer:

B. \(x + 7\)