Question

check your answers by 2. $a^2 + 11a + 30$

Explanation:

Step1: Find two numbers that multiply to 30 and add to 11.

We need two numbers \( m \) and \( n \) such that \( m \times n = 30 \) and \( m + n = 11 \). The numbers 5 and 6 work because \( 5\times6 = 30 \) and \( 5 + 6 = 11 \).

Step2: Factor the quadratic expression.

Using the numbers 5 and 6, we can rewrite the middle term and factor by grouping:
\[

$$\begin{align*} a^{2}+11a + 30&=a^{2}+5a+6a + 30\\ &=a(a + 5)+6(a + 5)\\ &=(a + 5)(a + 6) \end{align*}$$

\]

Answer:

\((a + 5)(a + 6)\)