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: x² + 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)

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