Steps for Factoring a Quadratic Trinomial

A quadratic trinomial in the form x^2 + bx + c can be factored by finding two numbers that:

1. Multiply to the constant term $c$.
2. Add up to the coefficient of the middle term b.

Once you find those two numbers:

• Rewrite the trinomial as a product of two binomials using these numbers.

Example 1

Factor: x^2 + 15x + 56

1. Find two numbers that multiply to $56$ and add up to $15$.
   • The numbers 7 and 8 work because 7×8=56 and 7+8 = 15.
2. Rewrite the trinomial as a product of binomials: x^2+15x+56=(x+7)(x+8)

Example 2

Factor: $x$

1. Find two numbers that multiply to 35 and add up to 12.
   • The numbers 5 and $7$ work because 5×7=35 and 5+7 = $12$.
2. Rewrite the trinomial as a product of binomials: x^2+12x+35=(x+5)(x+7)