FACTORING USING GROUPING STEPS

Step 5: Determine if any of the remaining factors can be factored further. In this case they can not so the final answer is

(X - 5) (X² + 3)

Step 6: Find the roots (zeros) by setting each factor equal to zero and solving for x.

X - 5=0 X² + 3=0 +5= +5 -3=-3 X = +5 X² = -3 take square root both sides X= square root -3

Step 3: Factor out the GCF from each of the two groups. In this problem, the signs in front of the 5x2 and the 15 are different, so you need to factor out a positive 3

X² (X - 5) + 3(X - 5)

Step 4: Notice that what is inside the parenthesis is a perfect match, so it is time for the 2 for 1 special. The one thing that the two groups have in common is (x - 5), so you can factor out (x - 5) leaving the following:

X² (X - 5) + 3(X - 5) (X - 5) (X² + 3)

Step 1: Decide if the four terms have anything in common, called the greatest common factor or GCF. If so, factor out the GCF. Do not forget to include the GCF as part of your final answer. In this case, the four terms only have a 1 in common which is of no help.

X³ - 5X² + 3X - 15

Step 2: Create smaller groups within the problem, usually done by grouping the first two terms together and the last two terms together

X³ - 5X² + 3X - 15