Given that (x+3) is a factor of the expression x^3 + 4x^2 + px + 3 , find the value

Step-by-step explanation:

We are given (x+3) is a factor of , which means if were to plug in -3, the result is 0.

Let's write that down:

So the cubic equation is actually that they wish we solve for .

To find another factor of the given cubic expression on the left, I'm going to use synthetic division with that polynomial and (x+3) where (x+3) is divisor.  Since (x+3) is the divisor, -3 will be on the outside like so:

-3 |  1    4    4     3

   |       -3   -3    -3

     ---------------------

      1      1     1      0

So the other factor of is .

We must solve .

Compare this to .

We have .

The quadratic formula is

.

Plug in the numbers we have for .

.

Simplify inside the square root while also performing the one operation on bottom:

Now our answer will include an imaginary part because of that sqrt(negative number).

The imaginary unit is .

So our final answer is:

45 units

Step-by-step explanation:

Since both figures are similar, the ratio of their similar sides will be equal to a constant. Hence;

8/10 = 12/EH

8EH = 12 * 10

8EH = 120

EH = 120/8

EH = 15

Perimeter of EFGH = 15 + 10 + 5 + 15 = 45 units