Question

Many trinomials of the form $x^2+bx+c$factor into the product of two binomials$\left(x+m\right)\left(x+n\right)$

Explain how you find the values of m and n.

Short answer

The value of $m$and $n$can be obtained by factorize$c.$

Step-by-step solution

Step 1. Given Information

Given that$x^2+bx+c$can be factors as$x^2+bx+c=\left(x+m\right)\left(x+n\right)$

Step 2. Find the values of m and n

The value of $mandn$can be obtained as

Write two factors as two binomials with first term $x.$

Find two numbers when they multiplied the result is $c$and then add the result is $b.$

Such that$$\begin{gathered} m\times n=c \\ m+n=b \end{gathered}$$