What is the greatest common factor of the terms in the polynomial 12x^4 + 27x^3 + 6x^2?
a. 3x
b. 3x^2
c. 6x^2
d. 6x^4

The greatest common factor is B) 3x^2.

In order to find this, we must first look to see the smallest number of x's in a term. The final term 6x^2 (which could also be expressed as 6xx), has 2. Therefore we know we can take out x^2.

The next thing we look for is a number that goes in evenly to all terms. It's easiest to start with the smallest number and it's factors. 6 is the smallest number and it's factors are 6, 3, 2, 1.

Since 6 does not go in evenly to 27, we try 3. 3 goes in evenly to both 27 and 12. Therefore, we can use 3.

The end result is 3x^2

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

step-by-step explanation:

graph using a few selected

x         y

-1       15

0         6

1         2.4

2       0.96