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:

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12