Factoring Trinomials by Grouping

Property To factor a trinomial $ax^2 + bx + c$, first find two factors of the product $ac$ that have a sum equal to $b$. Then rewrite the trinomial as a four term polynomial using these factors and factor by grouping. Explanation This is a magic trick to turn a tricky trinomial into an easy four term polynomial we already know how to solve! Multiply 'a' and 'c', then find two secret numbers that multiply to that product and add up to 'b'. Use these numbers to split the middle term into two, then use your regular grouping skills to win! Examples To factor $x^2 + 3x 10$, find factors of $1 \cdot ( 10) = 10$ that sum to $3$. They are $5$ and $ 2$. $x^2 + 5x 2x 10 = x(x+5) 2(x+5) = (x+5)(x 2)$ To factor $2k^2 7k + 6$, find factors of $2 \cdot 6 = 12$ that sum to $ 7$. They are $ 3$ and $ 4$. So, $2k^2 3k 4k+6 = k(2k 3) 2(2k 3) = (2k 3)(k 2)$.