Johnny is given 3 quartic equations to solve that are already written in standard form.  For one question, he has to take out a GCF first, for another question, he has to factor by grouping, and for the last question, he realizes that this is a special type of quartic equation that can be factored like a quadratic equation. State the characteristics that each of the equations have in order for the above methods to be used.

Solve for x.

x2+9x+18=0

Possible Answers:

x = –2

Cannot be factored by grouping

x = –6, –3

x = 6, 3

x = –9, –2

Correct

x = –6, –3

Explanation:

x2+9x+18=0

1) This is a relatively standard quadratic equation. List and add factors of 18.

1 + 18 = 19

2 + 9 = 11

3 + 6 = 9

x2+3x+6x+18=0

2) Pull out common factors of each pair, "x" from the first and "6" from the second.

x(x+3)+6(x+3)=0

3) Factor again, pulling out "(x+3)" from both terms.

(x+3)(x+6)=0

4) Set each term equal to zero and solve.

x + 3 = 0, x = –3

x + 6 = 0, x = –6

Step-by-step explanation: