Draft:AC Method

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Last edited by TarnishedPath (talk | contribs) 4 days ago. (Update)

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AC method is a technique used in algebra to factor quadratic trinomials of the form $ax^{2}+bx+c$ , where ( a ), the coefficient of $x^{2}$ , is not equal to 1.The method works by multiplying ( a ) and ( c ) to find their product, then identifying two numbers that multiply to this product and add up to ( b ); these numbers are used to split the middle term.^[1]

Steps

To divide a quadratic equation such as $Ax^{2}+Bx+C$ using the AC method, first multiply $A$ and $C$ . Here, $A$ is the coefficient of $x^{2}$ , and $C$ is the constant term.

For example, in the case of $6x^{2}+11x+3$ , $A=6$ , $C=3$ , so $AC=18$ .

Then, two numbers must be found whose product is $AC$ (here $18$ ) and whose sum is $B$ (here $11$ ). In this case, $9$ and $2$ work, because $9\times 2=18$ and $9+2=11$ .

Then the middle term has to be split using these two numbers. That is, $11x$ will become $9x+2x$ . As a result, the equation will become $6x^{2}+9x+2x+3$ .