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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 2nd degree polynomial in one variable (the highest power of the variable is 2).

3)      The linear term in a polynomial is the 1st 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)
 

 

MORE EXAMPLES:        (Click here to enlarge)

 

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