AC Method

AC method is a technique used in algebra to factor quadratic trinomials of the form $a{x}^2+bx+c$, 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.

Steps

To divide a quadratic equation such as $A{x}^2+Bx+C$ 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 $6x^2+9x+2x+3$.

Next, factor by grouping: from $(6x^2+9x)+(2x+3)$, we get $3x(2x+3)+1(2x+3)$.

Finally, take out the common factor and write the final form. Here, it is $(3x+1)(2x+3)$.

References

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