Factoring Trinomials: Positive C

Property To factor a trinomial $x^2 + bx + c$ where $c 0$, find two numbers that have a product of $c$ and a sum of $b$. Both numbers will be positive if $b$ is positive, and both will be negative if $b$ is negative. Explanation Imagine you're a detective looking for two number suspects! Your clues are the $b$ and $c$ values. When $c$ is positive, you know the suspects are partners in crime with the same sign. If $b$ is positive, they are a pair of positive heroes. If $b$ is negative, they are a duo of negative villains. Find the pair that multiplies to $c$ and adds to $b$! Examples To factor $x^2 + 10x + 21$, find two positive numbers that multiply to 21 and add to 10. The numbers are 3 and 7, so the factors are $(x+3)(x+7)$. To factor $x^2 11x + 24$, find two negative numbers that multiply to 24 and add to 11. The numbers are 3 and 8, so the factors are $(x 3)(x 8)$.