{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
{{ searchError }}
search
{{ courseTrack.displayTitle }}
{{ printedBook.courseTrack.name }} {{ printedBook.name }}

## Factoring Quadratics 1.17 - Solution

To factor a trinomial with a leading coefficient of $1,$ we need to find two numbers whose product is the independent term. $\begin{gathered} x^2+5x+\textcolor{#ff8c00}{6} \end{gathered}$ In this case, we have that the constant term is $\textcolor{#ff8c00}{6}.$ This is a positive number, so for a product to be positive, the factors must have the same sign (both positive or both negative).

Factor Constants Product of Constants
$1$ and $6$ $\textcolor{#ff8c00}{6}$
$\text{-}1$ and $\text{-}6$ $\textcolor{#ff8c00}{6}$
$2$ and $3$ $\textcolor{#ff8c00}{6}$
$\text{-}2$ and $\text{-}3$ $\textcolor{#ff8c00}{6}$

Next, let's consider the coefficient of the linear term. $\begin{gathered} x^2+\textcolor{#ff00ff}{5}x+6 \end{gathered}$ In this case, since the linear coefficient is $\textcolor{#ff00ff}{5},$ we need the sum of the factors to be $\textcolor{#ff00ff}{5}.$

Factors Sum of Factors
$1$ and $6$ $7$
$\text{-}1$ and $\text{-}6$ $\text{-}7$
$2$ and $3$ $\textcolor{#ff00ff}{5}$
$\text{-}2$ and $\text{-}3$ $\text{-}5$
We found two numbers whose product is $\textcolor{#ff8c00}{6}$ and whose sum is $\textcolor{#ff00ff}{5}.$ These numbers are $2$ and $3.$ With this we can factor the given trinomial.
$x^2+5x+6$
$x^2+2x+3x+6$
$x(x+2)+3x+6$
$x(x+2)+3(x+2)$
$(x+2)(x+3)$