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

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

To factor a trinomial of the form $x^2 + bx + c$ , follow a four-step procedure. First, write the factors as two binomials, each beginning with the variable $x$ : $(x\quad)(x\quad)$ . Second, find two numbers, $m$ and $n$ , that multiply to the constant term $c$ ( $m \cdot n = c$ ) and add up to the middle coefficient $b$ ( $m + n = b$ ). Third, use these two numbers, $m$ and $n$ , as the second terms of the binomial factors, giving the factored form $(x + m)(x + n)$ . Finally, check the result by multiplying the two binomial factors to ensure their product equals the original trinomial.

Updated 2026-04-30

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OpenStax Intermediate Algebra

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