# Factoring(3): Factoring Quadratic Trinomials With a Leading Coefficient of 1

Recall:

1) A trinomial is a polynomial with three terms.

2) A quadratic polynomial is a 2^{nd} degree polynomial in one variable (the highest power of the variable is 2).

3) The *linear* term in a polynomial is the 1^{st} degree term (the exponent of the variable is 1).

4) The *constant* term in a polynomial is the term without a variable.

5) “Coefficient” means the number part of a term.

6) “Sum” means the result of addition

7) “Product” means the result of addition

**HOW TO FACTOR A QUADRATIC TRINOMIAL WITH A LEADING COEFFICIENT OF 1:**

**1)** Make sure that the polynomial is, in fact, in the correct form: *x*^{2} + *bx* + *c*

(**Note:** Since we can’t see the coefficient of the first term, we know the leading coefficient is 1)

**2)** Think of two numbers, *p* and *q*, whose SUM is the coefficient of the linear term (*b*) and whose PRODUCT is the constant term (*c*).

**3)** Write the binomial factors – both factors begin with *x*, one factor ends with *p*, and one factor ends with *q*.

(**Note:** Because of the commutative property, the order of the factors doesn’t matter)

**EXAMPLES WITH EXPLANATIONS: **(Click here to enlarge)

**MORE EXAMPLES: **(Click here to enlarge)