What if you had a quadratic expression like in which all the coefficients were positive? How could you factor that expression? After completing this Concept, you'll be able to factor quadratic expressions like this one with positive coefficient values.
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CK12 Foundation: 0908S Factoring Quadratic Expressions
Guidance
Quadratic polynomials are polynomials of the degree. The standard form of a quadratic polynomial is written as
where and stand for constant numbers. Factoring these polynomials depends on the values of these constants. In this section we’ll learn how to factor quadratic polynomials for different values of and . (When none of the coefficients are zero, these expressions are also called quadratic trinomials , since they are polynomials with three terms.)
You’ve already learned how to factor quadratic polynomials where . For example, for the quadratic , the common factor is and this expression is factored as . Now we’ll see how to factor quadratics where is nonzero.
Factor when a = 1, b is Positive, and c is Positive
First, let’s consider the case where is positive and is positive. The quadratic trinomials will take the form
You know from multiplying binomials that when you multiply two factors , you get a quadratic polynomial. Let’s look at this process in more detail. First we use distribution:
Then we simplify by combining the like terms in the middle. We get:
So to factor a quadratic, we just need to do this process in reverse.
This means that we need to find two numbers and where
The factors of are always two binomials
such that and .
Example A
Factor .
Solution
We are looking for an answer that is a product of two binomials in parentheses:
We want two numbers and that multiply to 6 and add up to 5. A good strategy is to list the possible ways we can multiply two numbers to get 6 and then see which of these numbers add up to 5:
So the answer is .
We can check to see if this is correct by multiplying :
The answer checks out.
Example B
Factor .
Solution
We are looking for an answer that is a product of two binomials in parentheses:
The number 12 can be written as the product of the following numbers:
The answer is .
Example C
Factor .
Solution
We are looking for an answer that is a product of two binomials in parentheses:
The number 12 can be written as the product of the following numbers:
The answer is .
Watch this video for help with the Examples above.
CK12 Foundation: Factoring Quadratic Expressions
Vocabulary
 A quadratic of the form factors as a product of two binomials in parentheses:
 If and are positive, then both and are positive.
Guided Practice
Factor .
Solution
We are looking for an answer that is a product of two binomials in parentheses:
The number 36 can be written as the product of the following numbers:
The answer is .
Explore More
Factor the following quadratic polynomials.

x2+10x+9 
x2+15x+50 
x2+10x+21 
x2+16x+48 
x2+14x+45 
x2+27x+50 
x2+22x+40 
x2+15x+56 
x2+2x+1 
x2+10x+24 
x2+17x+72 
x2+25x+150