Is there a greatest common factor? What other factoring technique could you use according to the number of terms?
Prime
Practice makes perfect
We want to factor the given polynomial. Note that it has three terms.
5a^2-3a+15
First, notice that there is no greatest common factor. There are two additional common factoring techniques for trinomials.
General TrinomialsSince the first and the last terms are not perfect squares, we cannot use the perfect squares factoring. Now, let's check if we can apply the second method.
5a^2-3a+15
In this case, we have ac=5 * 15= 75. This is a positive number, so for the product of the constant terms in the factors to be positive, these constants must have the same sign (both positive or both negative.)
Factor Constants
Product of Constants
1 and 75
75
-1 and - 75
75
3 and 25
75
-3 and -25
75
5 and 15
75
-5 and -15
75
Next, let's consider the coefficient of the linear term.
5a^2 -3a+15
For this term, we need the sum of the factors that produced 75 to equal the coefficient of the linear term, -3.
Factors
Sum of Factors
1 and 75
76
-1 and -75
-76
3 and 25
28
-3 and -25
-28
5 and 15
20
-5 and -15
-20
As we can see, there are no such factors, whose product is 75 and sum equals - 3. Therefore, we cannot use the second method to factor the trinomial. This means, the given polynomial cannot be factored; it is prime.
Extra
Factoring techniques
There are different factoring techniques to apply according to the number of terms the polynomial has.
