Chapter 8.6, Problem 52HP

To determine

To compare the method of factoring the trinomial of the form $a{x}^2+bx+c$ to the method of factoring a trinomial of the form $x^2+bx+c$ . Also, discuss how to find the signs of the factors of $c$ .

Explanation of Solution

To factor a trinomial of the form $x^2+bx+c$ , look for the factors of $c$ which on adding gives the constant $b$ . Whereas to factor a trinomial of the form $a{x}^2+bx+c$ , first multiply the constants $a$ and $c$ , and then look for the factors of $ac$ which on addition gives the constant $b$ .

Once the factors $c$ are found, it will need to consider the positive as well as negative numbers. If the sign of $c$ is positive, then factors of $c$ must be either both positive or both negative. If the sign of $c$ is negative, the two factors of $c$ must of opposite signs.