Is there a greatest common factor? What other factoring technique could be used according to the number of terms?
2(b^2+6b-12)
Practice makes perfect
The greatest common factor (GCF) of an expression is a common factor of the terms in the expression. It is the common factor with the greatest coefficient and the greatest exponent. The GCF of the given expression is 2.
Since 12 is not a perfect square, we cannot write the given expression as perfect square trinomial. Let's try the other method. First, we will identify the values a, b, and c.
b^2+6b-12 ⇔ 1b^2+ 6b +( -12)
For our expression, we have that a= 1, b= 6, and c= - 12. We want to check if we can find a pair of integers with a product of a * c and a sum of b. In this case the product is 1( -12)=-12 and the sum is 6. Let's do it!
Factor Pair
Product
Sum
-1 and 12
-1* 12 - 12
-1+12 11
1 and -12
1* (-12) -12
1 +(-12) -11
-2 and 6
-2* 6 -12
-2+6 4
2 and -6
2* (-6) -12
2+(-6) -4
-3 and 4
-3* 4 - 12
-3+4 1
3 and -4
3* (-4) - 12
3+(-4) -1
We cannot find a pair of integers whose product is -12 and whose sum is 6. Therefore, we cannot general method for factoring trinomials. The given polynomial cannot be factored, so it is prime.
