Summary

__** Example 1: **__ 3x 2 +12x+12

1. Look for the Greatest Common Factor (GCF) and factor it out In this case 3x 2 +12x+12, the GCF is 3 3(x 2 +4x+4)

2. Look for the difference of squares. Since this problem has all positives and three numbers it is not the difference of squares

3. Look for perfect square Trinomials Since 4 is a perfect square, this is a perfect square trinomial 3(x+2) 2

4. CHECK YOUR WORK!!!

CHECKING: 1. Work with the sqared grouping first! 3(x+2)(x+2)

2. FOIL 3(x 2 +2x+2x+4)

3. Combine like terms 3(x 2 +4x+4)

4. Multiply by the Distributive Property (3 x x 2 )+(3 x 4x)+(3 x 4)

5. Simplify 3x 2 +12x+12

__** Example 2: **__ 3x 3 + 21x 2 + 36x

1. Look for the Greatest Common Factor (GCF) and factor it out In this case the GCF is 3x 3x(x 2 +7x+12)

2. Look for the difference of squares. Since this problem has all positives and three numbers it is not the difference of squares

3. Look for Perfect Square Trinomials

Since 12 is not a Perfect Square the Quadratic is not a Perfect Square Trinomial

4. Look at the coefficient infront of the quadratic term (__x2)__ In this case the coefficient of the quadratic term is 1, so we follow the rules of reverse FOIL-ing

3x(x 2 +7x+12)

3x(x+__)(x+__) we know that since both signs are plus that the sign in noth of the middles must be positive

5. Now we look at the last term Since the Last term has more than one two factors we have to look at all the posibilities

3x(x+1)(x+12) -OR- 3x(x+2)(x+6) -OR- 3x(x+3)(x+4)


 * Since both signs are + you do not need to worry about the order of the numbers**

6. FOIL each equasion. The prouduct of the FOILed equation that is the starting equation is the answer.

3x(x+1)(x+12) 3x(x 2 +1x+12x+12) 3x 3 +39x 2 +36x 2 Because the product is not that of the starting problem this is not the solution of the problem.

3x(x+2)(x+6) 3x(x2+12x+12)

3x 3 +36x 2 +36 This time the outer two are correct, but the middle term in too high so this is not our answer.

3x(x+3)(x+4) 3x(x 2 +7x+12) 3x 3 +21x 2 +36x This is the same problem as we started with so this is our answer.