1Cademy - Strategy for Factoring Trinomials of the Form $$x^2 + bx + c$$

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Strategy for Factoring Trinomials of the Form $x^2 + bx + c$

When factoring a trinomial of the form $x^2 + bx + c$ into two binomials $(x + m)(x + n)$ , first examine the signs of the trinomial's terms to determine the signs of the factors $m$ and $n$ . If the constant term $c$ is positive, the factors $m$ and $n$ must have the same sign. Specifically, if the middle coefficient $b$ is positive, both $m$ and $n$ are positive; if $b$ is negative, both $m$ and $n$ are negative. Conversely, if the constant term $c$ is negative, the factors $m$ and $n$ must have opposite signs. In this case where they have opposite signs, the sign of the factor with the larger absolute value will match the sign of the middle coefficient $b$ .