Q. 155 - Intermediate Algebra

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.

Step-by-Step Solution

Answer

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

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   a n d   n

The value of $m and n$ 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 $$\begin{gathered} m\times n=c \\ m+n=b \end{gathered}$$